Character formula for infinite-dimensional unitarizable modules of the general linear superalgebra

Journal of Algebra

Volumn 273, Issue 2, 2004, Pages 780-805

  Cheng, Shun Jen ^a   Lam, Ngau ^b   Zhang, R B ^c  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^b NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^c UNIVERSITY OF SYDNEY   (Australia)

Author keywords

Character formula; Howe duality; Lie superalgebra; Unitarizable representations

Indexed keywords

EID: 1442356448     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8693(03)00538-6     Document Type: Article

References (23)

1. A. Berele, A. Regev, Hook Young diagrams with applications to combinatorics and representations of Lie superalgebras, Adv. Math. 64 (1987) 118-175.
2. S.-J. Cheng, N. Lam, Infinite-dimensional Lie superalgebras and Hook Schur functions, math.RT/0206034, Comm. Math. Phys. 238 (2003) 95-118.
3. S.-J. Cheng, W. Wang, Howe duality for Lie superalgebras, Compositio Math. 128 (2001) 55-94.
4. S.-J. Cheng, W. Wang, Remarks on the Schur-Howe-Sergeev duality, Lett. Math. Phys. 52 (2000) 143-153.
5. S.-J. Cheng, W. Wang, Lie subalgebras of differential operators on the super circle, math.QA/0103092, Publ. Res. Inst. Math. Sci. 39 (2003) 545-600.
6. S.-J. Cheng, R.B. Zhang, Howe duality and combinatorial character formula for orthosymplectic Lie superalgebras, math.RT/0206036; Adv. Math., in press.
7. V.K. Dobrev, Positive energy unitary irreducible representations of D = 6 conformal supersymmetry, J. Phys. A 35 (2002) 7079-7100.
8. M. Davidson, E. Enright, R. Stanke, Differential operators and highest weight representations, Mem. Amer. Math. Soc. 94 (455) (1999).
9. R. D'Auria, S. Ferrara, M.A. Lled, V.S. Varadarajan, Spinor algebras, J. Geom. Phys. 40 (2001) 101-129.
10. T. Enright, Analogues of Kostant's u-cohomology formulas for unitary highest weight modules, J. Reine Angew. Math. 392 (1988) 27-36.
11. T. Enright, R. Howe, N. Wallach, A classification of unitary highest weight modules, in: Representation Theory of Reductive Groups, Park City, Utah, 1982, in: Progr. Math., vol. 40, Birkhäuser, Boston, MA, 1983, pp. 97-143.
12. R. Goodman, N. Wallach, Representations and Invariants of the Classical Groups, Cambridge University Press, Cambridge, 1998.
13. M.D. Gould, R.B. Zhang, Classification of all star irreps of gl(m n), J. Math. Phys. 31 (1990) 2552-2559.
14. R. Howe, Remarks on classical invariant theory, Trans. Amer. Math. Soc. 313 (1989) 539-570.
15. R. Howe, Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond, in: The Schur Lectures, Tel Aviv, in: Israel Math. Conf. Proc., vol. 8, 1992, pp. 1-182.
16. H.P. Jakobsen, The full set of unitarizable highest weight modules of basic classical Lie superalgebras, Mem. Amer. Math. Soc. 111 (532) (1994), pp. vi+116.
17. V. Kac, Lie superalgebras, Adv. Math. 16 (1977) 8-96.
18. M. Kashiwara, M. Vergne, On the Segal-Shale-Weil representations and harmonic polynomials, Invent. Math. 44 (1978) 1-47.
19. I.G. Macdonald, Symmetric Functions and Hall Polynomials, in: Oxford Math. Monogr., Clarendon, Oxford, 1995.
20. M. Nazarov, Quantum Berezinian and the classical Capelli identity, Lett. Math. Phys. 21 (2) (1991) 123-131.
21. n m, Nuovo Cimento 85 A (1985) 1-18.
22. A. Sergeev, An analog of the classical invariant theory for Lie superalgebras, I, II, Michigan Math. J. 49 (2001) 147-168.
23. P.K. Townsend, M-theory from its superalgebra, in: Strings, Branes and Dualities, Cargse, 1997, in: NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 520, Kluwer Academic, Dordrecht, 1999, pp. 141-177.