Littelmann path model (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Littelmann path model" in English language version.

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archive.org

Humphreys 1994 Humphreys, James E. (1994), Introduction to Lie Algebras and Representation Theory (2 ed.), Springer-Verlag, ISBN 0-387-90053-5

arxiv.org

Numerous authors have made contributions, including the physicist R. C. King, and the mathematicians S. Sundaram, I. M. Gelfand, A. Zelevinsky and A. Berenstein. The surveys of King (1990) and Sundaram (1990) give variants of Young tableaux which can be used to compute weight multiplicities, branching rules and tensor products with fundamental representations for the remaining classical Lie algebras. Berenstein & Zelevinsky (2001) discuss how their method using convex polytopes, proposed in 1988, is related to Littelmann paths and crystal bases. King, Ronald C. (1990), "S-functions and characters of Lie algebras and superalgebras", Institute for Mathematics and Its Applications, IMA Vol. Math. Appl., 19, Springer-Verlag: 226–261, Bibcode:1990IMA....19..226K Sundaram, Sheila (1990), "Tableaux in the representation theory of the classical Lie groups", Institute for Mathematics and Its Applications, IMA Vol. Math. Appl., 19, Springer-Verlag: 191–225, Bibcode:1990IMA....19..191S Berenstein, Arkady; Zelevinsky, Andrei (2001), "Tensor product multiplicities, canonical bases and totally positive varieties", Invent. Math., 143 (1): 77–128, arXiv:math/9912012, Bibcode:2001InMat.143...77B, doi:10.1007/s002220000102, S2CID 17648764

books.google.com

Weyl 1953 Weyl, Hermann (2016) [1953], The Classical Groups: Their Invariants and Representations (PMS-1), Princeton Landmarks in Mathematics and Physics, vol. 45 (2nd ed.), Princeton University Press, ISBN 978-1-4008-8390-5
Weyl 1953, p. 230,312. The "Brauer-Weyl rules" for restriction to maximal rank subgroups and for tensor products were developed independently by Brauer (in his thesis on the representations of the orthogonal groups) and by Weyl (in his papers on representations of compact semisimple Lie groups). Weyl, Hermann (2016) [1953], The Classical Groups: Their Invariants and Representations (PMS-1), Princeton Landmarks in Mathematics and Physics, vol. 45 (2nd ed.), Princeton University Press, ISBN 978-1-4008-8390-5
Littlewood 1950 Littlewood, Dudley E. (1977) [1950], The Theory of Group Characters and Matrix Representations of Groups, AMS Chelsea Publishing Series, vol. 357 (2nd ed.), American Mathematical Society, ISBN 978-0-8218-7435-6
Macdonald 1998 Macdonald, Ian G. (1998) [1979], Symmetric Functions and Hall Polynomials, Oxford mathematical monographs (2nd ed.), Clarendon Press, ISBN 978-0-19-850450-4

doi.org

Numerous authors have made contributions, including the physicist R. C. King, and the mathematicians S. Sundaram, I. M. Gelfand, A. Zelevinsky and A. Berenstein. The surveys of King (1990) and Sundaram (1990) give variants of Young tableaux which can be used to compute weight multiplicities, branching rules and tensor products with fundamental representations for the remaining classical Lie algebras. Berenstein & Zelevinsky (2001) discuss how their method using convex polytopes, proposed in 1988, is related to Littelmann paths and crystal bases. King, Ronald C. (1990), "S-functions and characters of Lie algebras and superalgebras", Institute for Mathematics and Its Applications, IMA Vol. Math. Appl., 19, Springer-Verlag: 226–261, Bibcode:1990IMA....19..226K Sundaram, Sheila (1990), "Tableaux in the representation theory of the classical Lie groups", Institute for Mathematics and Its Applications, IMA Vol. Math. Appl., 19, Springer-Verlag: 191–225, Bibcode:1990IMA....19..191S Berenstein, Arkady; Zelevinsky, Andrei (2001), "Tensor product multiplicities, canonical bases and totally positive varieties", Invent. Math., 143 (1): 77–128, arXiv:math/9912012, Bibcode:2001InMat.143...77B, doi:10.1007/s002220000102, S2CID 17648764
Littelmann 1997 Littelmann, Peter (1997), "Characters of Representations and Paths in ${\mathfrak {h}}$ _R*", Proceedings of Symposia in Pure Mathematics, 61, American Mathematical Society: 29–49, doi:10.1090/pspum/061/1476490 [instructional course]

harvard.edu

ui.adsabs.harvard.edu

Sundaram 1990 Sundaram, Sheila (1990), "Tableaux in the representation theory of the classical Lie groups", Institute for Mathematics and Its Applications, IMA Vol. Math. Appl., 19, Springer-Verlag: 191–225, Bibcode:1990IMA....19..191S
King 1990 King, Ronald C. (1990), "S-functions and characters of Lie algebras and superalgebras", Institute for Mathematics and Its Applications, IMA Vol. Math. Appl., 19, Springer-Verlag: 226–261, Bibcode:1990IMA....19..226K
Numerous authors have made contributions, including the physicist R. C. King, and the mathematicians S. Sundaram, I. M. Gelfand, A. Zelevinsky and A. Berenstein. The surveys of King (1990) and Sundaram (1990) give variants of Young tableaux which can be used to compute weight multiplicities, branching rules and tensor products with fundamental representations for the remaining classical Lie algebras. Berenstein & Zelevinsky (2001) discuss how their method using convex polytopes, proposed in 1988, is related to Littelmann paths and crystal bases. King, Ronald C. (1990), "S-functions and characters of Lie algebras and superalgebras", Institute for Mathematics and Its Applications, IMA Vol. Math. Appl., 19, Springer-Verlag: 226–261, Bibcode:1990IMA....19..226K Sundaram, Sheila (1990), "Tableaux in the representation theory of the classical Lie groups", Institute for Mathematics and Its Applications, IMA Vol. Math. Appl., 19, Springer-Verlag: 191–225, Bibcode:1990IMA....19..191S Berenstein, Arkady; Zelevinsky, Andrei (2001), "Tensor product multiplicities, canonical bases and totally positive varieties", Invent. Math., 143 (1): 77–128, arXiv:math/9912012, Bibcode:2001InMat.143...77B, doi:10.1007/s002220000102, S2CID 17648764

semanticscholar.org

api.semanticscholar.org

Numerous authors have made contributions, including the physicist R. C. King, and the mathematicians S. Sundaram, I. M. Gelfand, A. Zelevinsky and A. Berenstein. The surveys of King (1990) and Sundaram (1990) give variants of Young tableaux which can be used to compute weight multiplicities, branching rules and tensor products with fundamental representations for the remaining classical Lie algebras. Berenstein & Zelevinsky (2001) discuss how their method using convex polytopes, proposed in 1988, is related to Littelmann paths and crystal bases. King, Ronald C. (1990), "S-functions and characters of Lie algebras and superalgebras", Institute for Mathematics and Its Applications, IMA Vol. Math. Appl., 19, Springer-Verlag: 226–261, Bibcode:1990IMA....19..226K Sundaram, Sheila (1990), "Tableaux in the representation theory of the classical Lie groups", Institute for Mathematics and Its Applications, IMA Vol. Math. Appl., 19, Springer-Verlag: 191–225, Bibcode:1990IMA....19..191S Berenstein, Arkady; Zelevinsky, Andrei (2001), "Tensor product multiplicities, canonical bases and totally positive varieties", Invent. Math., 143 (1): 77–128, arXiv:math/9912012, Bibcode:2001InMat.143...77B, doi:10.1007/s002220000102, S2CID 17648764