Crystal graphs for Lie superalgebras and Cauchy decomposition

Journal of Algebraic Combinatorics

Volumn 25, Issue 1, 2007, Pages 57-100

  Kwon, Jae Hoon ^a  

^a University of Seoul   (South Korea)

Author keywords

Cauchy decomposition; Crystal graphs; Lie superalgebra

Indexed keywords

ALGEBRA; COMBINATORIAL MATHEMATICS; NUMERICAL METHODS;

BICRYSTAL GRAPH STRUCTURES; CAUCHY DECOMPOSITION; CRYSTAL GRAPHS; LIE SUPERALGEBRA;

GRAPH THEORY;

EID: 33845344396     PISSN: 09259899     EISSN: 15729192     Source Type: Journal    
DOI: 10.1007/s10801-006-0024-5     Document Type: Article

References (20)

1. q(gl(m, n))," J. Amer. Math. Soc. 13(2) (2000), 295-331.
2. A. Berele and A. Regev, "Hook Young diagrams with applications to combinatorics and to the representations of Lie superalgebras," Adv. Math. 64 (1987), 118-175.
3. S.-J. Cheng and N. Lam, "Infinite-dimensional Lie superalgebras and hook Schur functions," Comm. Math. Phys. 238(1-2) (2003), 95-118.
4. S.-J. Cheng and W. Wang, "Howe duality for Lie superalgebras," Compositio Math. 128(1) (2001), 55-94.
5. S.-J. Cheng and W. Wang, "Lie subalgebras of differential operators on the super circle," Publ. Res. Inst. Math. Sci. 39(3) (2003), 545-600.
6. V.I. Danilov and G.A. Koshevoy, "Bi-crystals and crystal (GL(V), GL(W)) duality," RIMS preprint, (2004) No. 1458.
7. W. Fulton, "Young tableaux," London Mathematical Society Student Texts, Vol. 35 Cambridge University Press," Cambridge, 1997.
8. K. Hasegawa, "Spin module versions of Weyl's reciprocity theorem for classical Kac-Moody Lie algebras - an application to branching rule duality," Publ. Res. Inst. Math. Sci. 25(5) (1989), 741-828.
9. R. Howe, "Remarks on classical invariant theory," Trans. Amer. Math. Soc. 313(2) (1989), 539-570.
10. V.G. Kac, Infinite Dimensional Lie Algebras. Cambridge University Press, 3rd ed., 1990.
11. V.G. Kac, "Lie superalgebras," Adv. in Math. 26(1) (1977), 8-96.
12. V.G. Kac and J.W. van de Leur, "Super boson-fermion correspondence," Ann. Inst. Fourier 37(4) (1987), 99-137.
13. 1+∞," Transform. Groups 1(1-2) (1996), 41-70.
14. q(gl(m, n))-modules," Comm. Math. Phys. 224 (2001), 705-732.
15. M. Kashiwara, "Crystal bases and Littelmann's refined Demazure character formula," Duke Math. J. 71 (1993), 839-858.
16. M. Kashiwara, "On crystal bases," Representations of groups, in CMS Conf. Proc., Vol. 16, Amer. Math. Soc., Providence, RI, (1995), pp. 155-197.
17. D. Knuth, "Permutations, matrices, and the generalized Young tableaux," Pacific J. Math. 34 (1970), 709-727.
18. I.G. Macdonald, "Symmetric functions and Hall polynomials," Oxford University Press, 2nd ed., 1995.
19. J.B. Remmel, "The combinatorics of (k, l)-hook Schur functions," Contemp. Math. 34 (1984), 253-287.
20. n," J. Combin. Theory Ser. A 46(1) (1987), 79-120.