表示论 (Chinese Wikipedia)

Analysis of information sources in references of the Wikipedia article "表示论" in Chinese language version.

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10ams.org

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1uni-goettingen.de

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ams.org

表示论的经典教材包括Curtis & Reiner (1962)和Serre (1977)。其它优质教材有Fulton & Harris (1991)和Goodman & Wallach (1998)。 Curtis, Charles W.; Reiner, Irving, Representation Theory of Finite Groups and Associative Algebras, John Wiley & Sons (Reedition 2006 by AMS Bookstore), 1962, ISBN 978-0-470-18975-7 . Serre, Jean-Pierre, Linear Representations of Finite Groups, Springer-Verlag, 1977, ISBN 978-0387901909 . Fulton, William; Harris, Joe, Representation theory. A first course, Graduate Texts in Mathematics, Readings in Mathematics 129, New York: Springer-Verlag, 1991, ISBN 978-0-387-97495-8, MR 1153249, ISBN 978-0-387-97527-6 . Goodman, Roe; Wallach, Nolan R., Representations and Invariants of the Classical Groups, Cambridge University Press, 1998, ISBN 978-0-521-66348-9 .
关于有限群表示论的历史，可见Lam (1998)；对代数群和李群表示的历史可见Borel (2001)。 Lam, T. Y., Representations of finite groups: a hundred years, Notices of the AMS (American Mathematical Society), 1998, 45 (3,4): 361–372 (Part I), 465–474 (Part II) . Borel, Armand, Essays in the History of Lie Groups and Algebraic Groups, American Mathematical Society, 2001, ISBN 978-0-8218-0288-5 .
Lam 1998，第372頁。 Lam, T. Y., Representations of finite groups: a hundred years, Notices of the AMS (American Mathematical Society), 1998, 45 (3,4): 361–372 (Part I), 465–474 (Part II) .
Fulton & Harris 1991, Simson, Skowronski & Assem 2007, Humphreys 1972。 Fulton, William; Harris, Joe, Representation theory. A first course, Graduate Texts in Mathematics, Readings in Mathematics 129, New York: Springer-Verlag, 1991, ISBN 978-0-387-97495-8, MR 1153249, ISBN 978-0-387-97527-6 . Simson, Daniel; Skowronski, Andrzej; Assem, Ibrahim, Elements of the Representation Theory of Associative Algebras, Cambridge University Press, 2007, ISBN 978-0-521-88218-7 .
这些内容可在大部分标准教材中找到，如Curtis & Reiner (1962)、Fulton & Harris (1991)、Goodman & Wallach (1998)、Gordon & Liebeck (1993)、Humphreys (1972)、Jantzen (2003)、Knapp (2001)、Serre (1977)等。 Curtis, Charles W.; Reiner, Irving, Representation Theory of Finite Groups and Associative Algebras, John Wiley & Sons (Reedition 2006 by AMS Bookstore), 1962, ISBN 978-0-470-18975-7 . Fulton, William; Harris, Joe, Representation theory. A first course, Graduate Texts in Mathematics, Readings in Mathematics 129, New York: Springer-Verlag, 1991, ISBN 978-0-387-97495-8, MR 1153249, ISBN 978-0-387-97527-6 . Goodman, Roe; Wallach, Nolan R., Representations and Invariants of the Classical Groups, Cambridge University Press, 1998, ISBN 978-0-521-66348-9 . Gordon, James; Liebeck, Martin, Representations and Characters of Finite Groups, Cambridge: Cambridge University Press, 1993, ISBN 978-0-521-44590-0 . Jantzen, Jens Carsten, Representations of Algebraic Groups, American Mathematical Society, 2003, ISBN 978-0-8218-3527-2 . Knapp, Anthony W., Representation Theory of Semisimple Groups: An Overview Based on Examples, Princeton University Press, 2001, ISBN 978-0-691-09089-4 . Serre, Jean-Pierre, Linear Representations of Finite Groups, Springer-Verlag, 1977, ISBN 978-0387901909 .
Alperin 1986、Lam 1998、Serre 1977。 Alperin, J. L., Local Representation Theory: Modular Representations as an Introduction to the Local Representation Theory of Finite Groups, Cambridge University Press, 1986, ISBN 978-0-521-44926-7 . Lam, T. Y., Representations of finite groups: a hundred years, Notices of the AMS (American Mathematical Society), 1998, 45 (3,4): 361–372 (Part I), 465–474 (Part II) . Serre, Jean-Pierre, Linear Representations of Finite Groups, Springer-Verlag, 1977, ISBN 978-0387901909 .
Fulton & Harris 1991。 Fulton, William; Harris, Joe, Representation theory. A first course, Graduate Texts in Mathematics, Readings in Mathematics 129, New York: Springer-Verlag, 1991, ISBN 978-0-387-97495-8, MR 1153249, ISBN 978-0-387-97527-6 .
Humphreys 1972b、Jantzen 2003。 Humphreys, James E., Linear Algebraic Groups, Graduate Texts in Mathematics 21, Berlin, New York: Springer-Verlag, 1972b, ISBN 978-0-387-90108-4, MR 0396773 Jantzen, Jens Carsten, Representations of Algebraic Groups, American Mathematical Society, 2003, ISBN 978-0-8218-3527-2 .
Mumford, Fogarty & Kirwan 1994。 Mumford, David; Fogarty, J.; Kirwan, F., Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)] 34 3rd, Berlin, New York: Springer-Verlag, 1994, ISBN 978-3-540-56963-3, MR 1304906
Gelbart 1984。 Gelbart, Stephen, An Elementary Introduction to the Langlands Program, Bulletin of the American Mathematical Society, 1984, 10 (2): 177–219 [2015-08-21], doi:10.1090/S0273-0979-1984-15237-6, （原始内容存档于2009-06-01） .

doi.org

Wigner 1939。 Wigner, Eugene P., On unitary representations of the inhomogeneous Lorentz group, 数学年刊 (Annals of Mathematics), 1939, 40 (1): 149–204, JSTOR 1968551, doi:10.2307/1968551 .
Peter & Weyl 1927。 Peter, F.; Weyl, Hermann, Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe, Mathematische Annalen, 1927, 97 (1): 737–755 [2015-08-21], doi:10.1007/BF01447892, （原始内容存档于2014-08-19） .
Bargmann 1947。 Bargmann, V., Irreducible unitary representations of the Lorenz group, 数学年刊 (Annals of Mathematics), 1947, 48 (3): 568–640, JSTOR 1969129, doi:10.2307/1969129 .
Kac 1977。 Kac, Victor G., Lie superalgebras, Advances in Mathematics, 1977, 26 (1): 8–96, doi:10.1016/0001-8708(77)90017-2 .
Gelbart 1984。 Gelbart, Stephen, An Elementary Introduction to the Langlands Program, Bulletin of the American Mathematical Society, 1984, 10 (2): 177–219 [2015-08-21], doi:10.1090/S0273-0979-1984-15237-6, （原始内容存档于2009-06-01） .

jstor.org

Wigner 1939。 Wigner, Eugene P., On unitary representations of the inhomogeneous Lorentz group, 数学年刊 (Annals of Mathematics), 1939, 40 (1): 149–204, JSTOR 1968551, doi:10.2307/1968551 .
Bargmann 1947。 Bargmann, V., Irreducible unitary representations of the Lorenz group, 数学年刊 (Annals of Mathematics), 1947, 48 (3): 568–640, JSTOR 1969129, doi:10.2307/1969129 .

uni-goettingen.de

gdz.sub.uni-goettingen.de

Peter & Weyl 1927。 Peter, F.; Weyl, Hermann, Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe, Mathematische Annalen, 1927, 97 (1): 737–755 [2015-08-21], doi:10.1007/BF01447892, （原始内容存档于2014-08-19） .

web.archive.org

Peter & Weyl 1927。 Peter, F.; Weyl, Hermann, Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe, Mathematische Annalen, 1927, 97 (1): 737–755 [2015-08-21], doi:10.1007/BF01447892, （原始内容存档于2014-08-19） .
Gelbart 1984。 Gelbart, Stephen, An Elementary Introduction to the Langlands Program, Bulletin of the American Mathematical Society, 1984, 10 (2): 177–219 [2015-08-21], doi:10.1090/S0273-0979-1984-15237-6, （原始内容存档于2009-06-01） .