Rational semistandard tableaux and character formula for the Lie superalgebra over(gl, ̂)∞ | ∞

Advances in Mathematics

Volumn 217, Issue 2, 2008, Pages 713-739

  Kwon, Jae Hoon ^a  

^a University of Seoul   (South Korea)

Author keywords

Character formula; Howe duality; Lie superalgebra; RSK correspondence; Semistandard tableau

Indexed keywords

EID: 36048971726     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2007.09.001     Document Type: Article

References (33)

1. Berele A., and Regev A. Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras. Adv. Math. 64 (1987) 118-175
2. Benkart G., Sottile F., and Stroomer J. Tableau switching: Algorithms and applications. J. Combin. Theory Ser. A 76 (1996) 11-43
3. Cheng S.-J., and Lam N. Infinite-dimensional Lie superalgebras and hook Schur functions. Comm. Math. Phys. 238 (2003) 95-118
4. Cheng S.-J., Lam N., and Zhang R.B. Character formula for infinite-dimensional unitarizable modules of the general linear superalgebra. J. Algebra 273 (2004) 780-805
5. Cheng S.-J., and Wang W. Howe duality for Lie superalgebras. Compos. Math. 128 (2001) 55-94
6. Cheng S.-J., and Wang W. Lie subalgebras of differential operators on the super circle. Publ. Res. Inst. Math. Sci. 39 (2003) 545-600
7. Cheng S.-J., and Zhang R.B. Howe duality and combinatorial character formula for orthosymplectic Lie superalgebras. Adv. Math. 182 (2004) 124-172
8. Frenkel I.B. Representations of Kac-Moody algebras and dual resonance models. Applications of Group Theory in Physics and Mathematical Physics. Lectures in Appl. Math. vol. 21 (1985), Amer. Math. Soc., Providence 325-353
9. N) with central charge N. Comm. Math. Phys. 170 (1995) 337-357
10. Fulton W. Young Tableaux. London Math. Soc. Stud. Texts vol. 35 (1997), Cambridge University Press, Cambridge
11. Haiman M. On mixed insertion, symmetry, and shifted Young tableaux. J. Combin. Theory Ser. A 50 (1989) 196-225
12. Hanlon P., and Sundaram S. On a bijection between Littlewood-Richardson fillings of conjugate shape. J. Combin. Theory Ser. A 60 (1992) 1-18
13. Howe R. Remarks on classical invariant theory. Trans. Amer. Math. Soc. 313 (1989) 539-570
14. R. Howe, Perspectives on Invariant Theory: Schur duality, multiplicity free actions and beyond, The Schur Lectures, Israel Mathematical Conference Proceedings, vol. 8, Tel Aviv, 1992, pp. 1-182
15. Kac V.G. Lie superalgebras. Adv. Math. 26 (1977) 8-96
16. Kac V.G., and van de Leur J.W. Super boson-fermion correspondence. Ann. Inst. Fourier 37 (1987) 99-137
17. Kac V.G., and Radul A. Quasi-finite highest weight modules over the Lie algebras of differential operators on the circle. Comm. Math. Phys. 158 (1993) 429-457
18. 1 + ∞. Transform. Groups 1 (1996) 41-70
19. q (gl (m, n))-modules. Comm. Math. Phys. 224 (2001) 705-732
20. Kashiwara M., and Vergne M. On the Segal-Shale-Weil representations and harmonic polynomials. Invent. Math. 44 (1978) 1-47
21. Kwon J.-H. Crystal graphs for Lie superalgebras and Cauchy decomposition. J. Algebraic Combin. 25 (2007) 57-100
22. Knuth D. Permutations, matrices, and generalized Young tableaux. Pacific J. Math. 34 (1970) 709-727
23. Leites D., and Shchepochkina I. The Howe duality and Lie superalgebras. math.RT/0202181
24. Lam N., and Zhang R.B. Quasi-finite modules for Lie superalgebras of infinite rank. Trans. Amer. Math. Soc. 358 (2006) 403-439
25. Macdonald I.G. Symmetric Functions and Hall Polynomials. second ed. (1995), Oxford University Press
26. Nishiyama K. Super dual pairs and highest weight modules of orthosymplectic algebras. Adv. Math. 104 (1994) 66-89
27. Remmel J.B. The combinatorics of (k, l)-hook Schur functions. Contemp. Math. vol. 34 (1984) 253-287
28. n. J. Combin. Theory Ser. A 46 (1987) 79-120
29. Stroomer J. Insertion and the multiplication of rational Schur functions. J. Combin. Theory Ser. A 65 (1994) 79-116
30. Thomas G.P. On Schensted's construction and the multiplication of Schur functions. Adv. Math. 30 (1978) 8-32
31. Wang W. Duality in infinite-dimensional Fock representations. Commun. Contemp. Math. 1 (1999) 155-199
32. 1 + ∞. J. Algebra 216 (1999) 159-177
33. Zelevinsky A. Representations of Finite Classical Groups: A Hopf Algebra Approach. Springer Lecture Notes vol. 869 (1981)