Representation theory (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Representation theory" in English language version.

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Classic texts on representation theory include Curtis & Reiner (1962) and Serre (1977). Other excellent sources are Fulton & Harris (1991) and Goodman & Wallach (1998). Curtis, Charles W.; Reiner, Irving (1962), Representation Theory of Finite Groups and Associative Algebras, John Wiley & Sons (Reedition 2006 by AMS Bookstore), ISBN 978-0-470-18975-7. Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Springer-Verlag, ISBN 978-0387901909. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.. Goodman, Roe; Wallach, Nolan R. (1998), Representations and Invariants of the Classical Groups, Cambridge University Press, ISBN 978-0-521-66348-9.
Fulton & Harris 1991, Simson, Skowronski & Assem 2007, Humphreys 1972a. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.. Simson, Daniel; Skowronski, Andrzej; Assem, Ibrahim (2007), Elements of the Representation Theory of Associative Algebras, Cambridge University Press, ISBN 978-0-521-88218-7. Humphreys, James E. (1972a), Introduction to Lie Algebras and Representation Theory, Birkhäuser, ISBN 978-0-387-90053-7.
This material can be found in standard textbooks, such as Curtis & Reiner (1962), Fulton & Harris (1991), Goodman & Wallach (1998), James & Liebeck (1993), Humphreys (1972a), Jantzen (2003), Knapp (2001) and Serre (1977). Curtis, Charles W.; Reiner, Irving (1962), Representation Theory of Finite Groups and Associative Algebras, John Wiley & Sons (Reedition 2006 by AMS Bookstore), ISBN 978-0-470-18975-7. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.. Goodman, Roe; Wallach, Nolan R. (1998), Representations and Invariants of the Classical Groups, Cambridge University Press, ISBN 978-0-521-66348-9. James, Gordon; Liebeck, Martin (1993), Representations and Characters of Groups, Cambridge: Cambridge University Press, ISBN 978-0-521-44590-0. Humphreys, James E. (1972a), Introduction to Lie Algebras and Representation Theory, Birkhäuser, ISBN 978-0-387-90053-7. Jantzen, Jens Carsten (2003), Representations of Algebraic Groups, American Mathematical Society, ISBN 978-0-8218-3527-2. Knapp, Anthony W. (2001), Representation Theory of Semisimple Groups: An Overview Based on Examples, Princeton University Press, ISBN 978-0-691-09089-4. Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Springer-Verlag, ISBN 978-0387901909.
Fulton & Harris 1991. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103..
Humphreys 1972b, Jantzen 2003. Humphreys, James E. (1972b), Linear Algebraic Groups, Graduate Texts in Mathematics, vol. 21, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90108-4, MR 0396773 Jantzen, Jens Carsten (2003), Representations of Algebraic Groups, American Mathematical Society, ISBN 978-0-8218-3527-2.
Mumford, Fogarty & Kirwan 1994. Mumford, David; Fogarty, J.; Kirwan, F. (1994), Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)], vol. 34 (3rd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-540-56963-3, MR 0214602; MR 0719371 (2nd ed.); MR 1304906(3rd ed.)

ams.org

For the history of the representation theory of finite groups, see Lam (1998). For algebraic and Lie groups, see Borel (2001). Lam, T. Y. (1998), "Representations of finite groups: a hundred years", Notices of the AMS, 45 (3, 4): 361–372 (Part I), 465–474 (Part II). Borel, Armand (2001), Essays in the History of Lie Groups and Algebraic Groups, American Mathematical Society, ISBN 978-0-8218-0288-5.
Lam 1998, p. 372. Lam, T. Y. (1998), "Representations of finite groups: a hundred years", Notices of the AMS, 45 (3, 4): 361–372 (Part I), 465–474 (Part II).
Alperin 1986, Lam 1998, Serre 1977. Alperin, J. L. (1986), Local Representation Theory: Modular Representations as an Introduction to the Local Representation Theory of Finite Groups, Cambridge University Press, ISBN 978-0-521-44926-7. Lam, T. Y. (1998), "Representations of finite groups: a hundred years", Notices of the AMS, 45 (3, 4): 361–372 (Part I), 465–474 (Part II). Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Springer-Verlag, ISBN 978-0387901909.

archive.org

Classic texts on representation theory include Curtis & Reiner (1962) and Serre (1977). Other excellent sources are Fulton & Harris (1991) and Goodman & Wallach (1998). Curtis, Charles W.; Reiner, Irving (1962), Representation Theory of Finite Groups and Associative Algebras, John Wiley & Sons (Reedition 2006 by AMS Bookstore), ISBN 978-0-470-18975-7. Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Springer-Verlag, ISBN 978-0387901909. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.. Goodman, Roe; Wallach, Nolan R. (1998), Representations and Invariants of the Classical Groups, Cambridge University Press, ISBN 978-0-521-66348-9.
Sternberg 1994. Sternberg, Shlomo (1994), Group Theory and Physics, Cambridge University Press, ISBN 978-0-521-55885-3.
Fulton & Harris 1991, Simson, Skowronski & Assem 2007, Humphreys 1972a. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.. Simson, Daniel; Skowronski, Andrzej; Assem, Ibrahim (2007), Elements of the Representation Theory of Associative Algebras, Cambridge University Press, ISBN 978-0-521-88218-7. Humphreys, James E. (1972a), Introduction to Lie Algebras and Representation Theory, Birkhäuser, ISBN 978-0-387-90053-7.
This material can be found in standard textbooks, such as Curtis & Reiner (1962), Fulton & Harris (1991), Goodman & Wallach (1998), James & Liebeck (1993), Humphreys (1972a), Jantzen (2003), Knapp (2001) and Serre (1977). Curtis, Charles W.; Reiner, Irving (1962), Representation Theory of Finite Groups and Associative Algebras, John Wiley & Sons (Reedition 2006 by AMS Bookstore), ISBN 978-0-470-18975-7. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.. Goodman, Roe; Wallach, Nolan R. (1998), Representations and Invariants of the Classical Groups, Cambridge University Press, ISBN 978-0-521-66348-9. James, Gordon; Liebeck, Martin (1993), Representations and Characters of Groups, Cambridge: Cambridge University Press, ISBN 978-0-521-44590-0. Humphreys, James E. (1972a), Introduction to Lie Algebras and Representation Theory, Birkhäuser, ISBN 978-0-387-90053-7. Jantzen, Jens Carsten (2003), Representations of Algebraic Groups, American Mathematical Society, ISBN 978-0-8218-3527-2. Knapp, Anthony W. (2001), Representation Theory of Semisimple Groups: An Overview Based on Examples, Princeton University Press, ISBN 978-0-691-09089-4. Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Springer-Verlag, ISBN 978-0387901909.
Serre 1977. Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Springer-Verlag, ISBN 978-0387901909.
Alperin 1986, Lam 1998, Serre 1977. Alperin, J. L. (1986), Local Representation Theory: Modular Representations as an Introduction to the Local Representation Theory of Finite Groups, Cambridge University Press, ISBN 978-0-521-44926-7. Lam, T. Y. (1998), "Representations of finite groups: a hundred years", Notices of the AMS, 45 (3, 4): 361–372 (Part I), 465–474 (Part II). Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Springer-Verlag, ISBN 978-0387901909.
Serre 1977, Part III. Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Springer-Verlag, ISBN 978-0387901909.
Humphreys 1972a. Humphreys, James E. (1972a), Introduction to Lie Algebras and Representation Theory, Birkhäuser, ISBN 978-0-387-90053-7.

berkeley.edu

math.berkeley.edu

Teleman, Constantin (2005). "Representation Theory" (PDF). math.berkeley.edu. Retrieved 2019-12-09.

britannica.com

Ronan, Mark Andrew. "linear algebra". Encyclopedia Britannica. Retrieved 8 July 2024. linear algebra is very well understood

doi.org

Classic texts on representation theory include Curtis & Reiner (1962) and Serre (1977). Other excellent sources are Fulton & Harris (1991) and Goodman & Wallach (1998). Curtis, Charles W.; Reiner, Irving (1962), Representation Theory of Finite Groups and Associative Algebras, John Wiley & Sons (Reedition 2006 by AMS Bookstore), ISBN 978-0-470-18975-7. Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Springer-Verlag, ISBN 978-0387901909. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.. Goodman, Roe; Wallach, Nolan R. (1998), Representations and Invariants of the Classical Groups, Cambridge University Press, ISBN 978-0-521-66348-9.
Borel & Casselman 1979, Gelbart 1984. Borel, Armand; Casselman, W. (1979), Automorphic Forms, Representations, and L-functions, American Mathematical Society, ISBN 978-0-8218-1435-2. Gelbart, Stephen (1984), "An Elementary Introduction to the Langlands Program", Bulletin of the American Mathematical Society, 10 (2): 177–219, doi:10.1090/S0273-0979-1984-15237-6.
Fulton & Harris 1991, Simson, Skowronski & Assem 2007, Humphreys 1972a. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.. Simson, Daniel; Skowronski, Andrzej; Assem, Ibrahim (2007), Elements of the Representation Theory of Associative Algebras, Cambridge University Press, ISBN 978-0-521-88218-7. Humphreys, James E. (1972a), Introduction to Lie Algebras and Representation Theory, Birkhäuser, ISBN 978-0-387-90053-7.
This material can be found in standard textbooks, such as Curtis & Reiner (1962), Fulton & Harris (1991), Goodman & Wallach (1998), James & Liebeck (1993), Humphreys (1972a), Jantzen (2003), Knapp (2001) and Serre (1977). Curtis, Charles W.; Reiner, Irving (1962), Representation Theory of Finite Groups and Associative Algebras, John Wiley & Sons (Reedition 2006 by AMS Bookstore), ISBN 978-0-470-18975-7. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.. Goodman, Roe; Wallach, Nolan R. (1998), Representations and Invariants of the Classical Groups, Cambridge University Press, ISBN 978-0-521-66348-9. James, Gordon; Liebeck, Martin (1993), Representations and Characters of Groups, Cambridge: Cambridge University Press, ISBN 978-0-521-44590-0. Humphreys, James E. (1972a), Introduction to Lie Algebras and Representation Theory, Birkhäuser, ISBN 978-0-387-90053-7. Jantzen, Jens Carsten (2003), Representations of Algebraic Groups, American Mathematical Society, ISBN 978-0-8218-3527-2. Knapp, Anthony W. (2001), Representation Theory of Semisimple Groups: An Overview Based on Examples, Princeton University Press, ISBN 978-0-691-09089-4. Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Springer-Verlag, ISBN 978-0387901909.
Wigner 1939. Wigner, Eugene P. (1939), "On unitary representations of the inhomogeneous Lorentz group", Annals of Mathematics, 40 (1): 149–204, Bibcode:1939AnMat..40..149W, doi:10.2307/1968551, JSTOR 1968551, S2CID 121773411.
Peter & Weyl 1927. Peter, F.; Weyl, Hermann (1927), "Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe", Mathematische Annalen, 97 (1): 737–755, doi:10.1007/BF01447892, S2CID 120013521.
Bargmann 1947. Bargmann, V. (1947), "Irreducible unitary representations of the Lorenz group", Annals of Mathematics, 48 (3): 568–640, doi:10.2307/1969129, JSTOR 1969129.
Pontrjagin 1934. Pontrjagin, Lev S. (1934), "The theory of topological commutative groups", Annals of Mathematics, 35 (2): 361–388, doi:10.2307/1968438, JSTOR 1968438.
Fulton & Harris 1991. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103..
Kac 1977. Kac, Victor G. (1977), "Lie superalgebras", Advances in Mathematics, 26 (1): 8–96, doi:10.1016/0001-8708(77)90017-2.
Gelbart 1984. Gelbart, Stephen (1984), "An Elementary Introduction to the Langlands Program", Bulletin of the American Mathematical Society, 10 (2): 177–219, doi:10.1090/S0273-0979-1984-15237-6.

harvard.edu

ui.adsabs.harvard.edu

Wigner 1939. Wigner, Eugene P. (1939), "On unitary representations of the inhomogeneous Lorentz group", Annals of Mathematics, 40 (1): 149–204, Bibcode:1939AnMat..40..149W, doi:10.2307/1968551, JSTOR 1968551, S2CID 121773411.

jstor.org

Wigner 1939. Wigner, Eugene P. (1939), "On unitary representations of the inhomogeneous Lorentz group", Annals of Mathematics, 40 (1): 149–204, Bibcode:1939AnMat..40..149W, doi:10.2307/1968551, JSTOR 1968551, S2CID 121773411.
Bargmann 1947. Bargmann, V. (1947), "Irreducible unitary representations of the Lorenz group", Annals of Mathematics, 48 (3): 568–640, doi:10.2307/1969129, JSTOR 1969129.
Pontrjagin 1934. Pontrjagin, Lev S. (1934), "The theory of topological commutative groups", Annals of Mathematics, 35 (2): 361–388, doi:10.2307/1968438, JSTOR 1968438.

mit.edu

www-math.mit.edu

Etingof, Pavel; Golberg, Oleg; Hensel, Sebastian; Liu, Tiankai; Schwendner, Alex; Vaintrob, Dmitry; Yudovina, Elena (January 10, 2011). "Introduction to representation theory" (PDF). www-math.mit.edu. Retrieved 2019-12-09.

ncatlab.org

"representation theory in nLab". ncatlab.org. Retrieved 2019-12-09.

semanticscholar.org

api.semanticscholar.org

Wigner 1939. Wigner, Eugene P. (1939), "On unitary representations of the inhomogeneous Lorentz group", Annals of Mathematics, 40 (1): 149–204, Bibcode:1939AnMat..40..149W, doi:10.2307/1968551, JSTOR 1968551, S2CID 121773411.
Peter & Weyl 1927. Peter, F.; Weyl, Hermann (1927), "Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe", Mathematische Annalen, 97 (1): 737–755, doi:10.1007/BF01447892, S2CID 120013521.

worldcat.org

search.worldcat.org

Classic texts on representation theory include Curtis & Reiner (1962) and Serre (1977). Other excellent sources are Fulton & Harris (1991) and Goodman & Wallach (1998). Curtis, Charles W.; Reiner, Irving (1962), Representation Theory of Finite Groups and Associative Algebras, John Wiley & Sons (Reedition 2006 by AMS Bookstore), ISBN 978-0-470-18975-7. Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Springer-Verlag, ISBN 978-0387901909. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.. Goodman, Roe; Wallach, Nolan R. (1998), Representations and Invariants of the Classical Groups, Cambridge University Press, ISBN 978-0-521-66348-9.
Fulton & Harris 1991, Simson, Skowronski & Assem 2007, Humphreys 1972a. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.. Simson, Daniel; Skowronski, Andrzej; Assem, Ibrahim (2007), Elements of the Representation Theory of Associative Algebras, Cambridge University Press, ISBN 978-0-521-88218-7. Humphreys, James E. (1972a), Introduction to Lie Algebras and Representation Theory, Birkhäuser, ISBN 978-0-387-90053-7.
This material can be found in standard textbooks, such as Curtis & Reiner (1962), Fulton & Harris (1991), Goodman & Wallach (1998), James & Liebeck (1993), Humphreys (1972a), Jantzen (2003), Knapp (2001) and Serre (1977). Curtis, Charles W.; Reiner, Irving (1962), Representation Theory of Finite Groups and Associative Algebras, John Wiley & Sons (Reedition 2006 by AMS Bookstore), ISBN 978-0-470-18975-7. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.. Goodman, Roe; Wallach, Nolan R. (1998), Representations and Invariants of the Classical Groups, Cambridge University Press, ISBN 978-0-521-66348-9. James, Gordon; Liebeck, Martin (1993), Representations and Characters of Groups, Cambridge: Cambridge University Press, ISBN 978-0-521-44590-0. Humphreys, James E. (1972a), Introduction to Lie Algebras and Representation Theory, Birkhäuser, ISBN 978-0-387-90053-7. Jantzen, Jens Carsten (2003), Representations of Algebraic Groups, American Mathematical Society, ISBN 978-0-8218-3527-2. Knapp, Anthony W. (2001), Representation Theory of Semisimple Groups: An Overview Based on Examples, Princeton University Press, ISBN 978-0-691-09089-4. Serre, Jean-Pierre (1977), Linear Representations of Finite Groups, Springer-Verlag, ISBN 978-0387901909.
Humphreys, James E. (1975). Linear Algebraic Groups. New York, NY: Springer New York. ISBN 978-1-4684-9443-3. OCLC 853255426.
Fulton & Harris 1991. Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103..

worldcat.org

Humphreys, James E. (1975). Linear Algebraic Groups. New York, NY: Springer New York. ISBN 978-1-4684-9443-3. OCLC 853255426.