Explicit Constructions of the Fundamental Representations of the Symplectic Lie Algebras
Tài liệu tham khảo
Berele, 1986, Construction of Sp-modules by tableaux, Linear and Multilinear Algebra, 19, 299, 10.1080/03081088608817725
De Concini, 1979, Symplectic standard tableaux, Adv. Math., 34, 1, 10.1016/0001-8708(79)90061-6
R. G. Donnelly, Explicit Constructions of Representations of Semisimple Lie Algebras, Ph.D. thesis, Univ. of North Carolina, 1997.
Donnelly, 1999, Symplectic analogs of L(m,n), J. Combin. Theory Ser. A, 88, 217, 10.1006/jcta.1999.2991
R. G. Donnelly, Supporting Graphs and Representation Diagrams for Representations of Semisimple Lie Algebras, in preparation.
Gelfand, 1950, Finite-dimensional representations of the group of unimodular matrices, Dokl. Acad. Nauk. USSR, 71, 825
Gelfand, 1950, Finite-dimensional representations of the group of orthogonal matrices, Dokl. Akad. Nauk. USSR, 71, 1017
Humphreys, 1972
Jantzen, 1996, 6
Kashiwara, 1994, Crystal graphs for representations of the q-analogue of classical Lie algebras, J. Algebra, 165, 295, 10.1006/jabr.1994.1114
King, 1993, Construction of orthogonal group modules using tableaux, Linear and Multilinear Algebra, 33, 251, 10.1080/03081089308818198
Molev, 1999, A basis for representations of symplectic Lie algebras, Comm. Math. Phys., 201, 591, 10.1007/s002200050570
A. Molev, A weight basis for representations of even orthogonal Lie algebras, in, Proceedings of the Kyoto Conference on Combinatorial Methods in Representation Theory, October/November 1998, to appear.
A. Molev, Weight bases of Gelfand–Tsetlin type for representations of classical Lie algebras, Preprint SMS 99-21, University of Sydney, September 1999.
Nazarov, 1994, Yangians and Gelfand–Tsetlin Bases, Publ. Res. Inst. Math. Sci., 30, 459, 10.2977/prims/1195165907
Proctor, 1982, Representations of sl(2,C) on posets and the Sperner property, SIAM J. Algebraic Discrete Methods, 3, 275, 10.1137/0603026
Proctor, 1984, Bruhat lattices, plane partition generating functions, and minuscule representations, European J. Combin., 5, 331, 10.1016/S0195-6698(84)80037-2
Proctor, 1982, Solution of two difficult combinatorial problems with linear algebra, Amer. Math. Monthly, 89, 721, 10.2307/2975833
Proctor, 1994, Young tableaux, Gelfand patterns, and branching rules for classical groups, J. Algebra, 164, 299, 10.1006/jabr.1994.1064
Proctor, 1990, Solution of a Sperner conjecture of Stanley with a construction of Gelfand, J. Combin. Theory Ser. A, 54, 225, 10.1016/0097-3165(90)90032-R
Reiner, 1998, Unimodality of differences of specialized Schur functions, J. Algebraic Combin., 7, 91, 10.1023/A:1008623312887
Sheats, 1999, A symplectic jeu de taquin bijection between the tableaux of King and of De Concini, Trans. Amer. Math. Soc., 351, 3569, 10.1090/S0002-9947-99-02166-2
Stanley, 1980, Weyl groups, the hard Lefschetz theorem, and the Sperner property, SIAM J. Algebraic Discrete Methods, 1, 168, 10.1137/0601021
Stanley, 1986