Finite dimensional representations of

Author:
Yi Ming Zou

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1607-1616

MSC (1991):
Primary 17B37; Secondary 81R50, 17B70

DOI:
https://doi.org/10.1090/S0002-9939-97-03757-X

MathSciNet review:
1371148

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Structures of the finite dimensional simple weight -modules are studied in detail for both the generic and the roots of 1 cases.

**1.**C. De Concini and V. Kac,*Representations of quantum groups at roots of 1*, Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, Progress in Math, vol. 92, Birkhauser, 1990, pp. 471-506. MR**92g:17012****2.**R. Floreanini, D. A. Leites, and L. Vinet,*On the defining relations of quantum superalgebras*, Lett. Math. Phys.**23**(1991), 127-131. MR**92m:17010****3.**R. Floreanini, V. P. Spiridonov, and L. Vinet,*-Oscillator realizations of the quantum superalgebras and*, Commun. Math. Phys.**137**(1991), 149-160. MR**92a:81075****4.**M. D. Gould and M. Scheunert,*Classification of finite dimensional unitary irreps for*, J. Math. Phys.**36**(1994), 435-452. MR**96e:17036****5.**V. Kac,*Lie superalgebras*, Adv. Math.**26**(1977), 8-96. MR**58:5803****6.**V. Kac,*Representations of classical Lie superalgebras*, Lecture Notes in Math., vol. 676, 1977, pp. 579-626. MR**80f:17006****7.**J. R. Links, and M. D. Gould,*Two variable link polynomials from quantum supergroups*, Lett. Math. Phys.**26**(1992), 187-198. MR**93k:57018****8.**G. Lusztig,*Quantum deformations of certain simple modules over enveloping algebras*, Adv. Math.**70**(1988), 237-249. MR**89k:17029****9.**-,*Quantum groups at roots of 1*, Geom. Ded.**35**(1990), 89-113. MR**91j:17018****10.**M. Scheunert,*Serre-type relations for special linear Lie superalgebras*, Lett. Math. Phys.**24**(1992), 173-181. MR**93d:17006****11.**M. Scheunert,*The presentation and deformation of special linear Lie superalgebras*, J. Math. Phys.**34**(8) (1993), 3780-3808. MR**94i:17007****12.**R. B. Zhang,*Braid group representations arising from quantum supergroups with arbitrary and link polynomials*, J. Math. Phys.**33**(11) (1992), 3918-3930. MR**94d:20040****13.**R. B. Zhang,*Finite-dimensional representations of and its connection with quantum ,*Lett. Math. Phys.**25**(1992), 317-325. MR**93k:17042****14.**Y. M. Zou,*Deformations of enveloping algebra of Lie superalgebra*, Commun. Math. Phys.**162**(3) (1994), 467-479. MR**95h:17014**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
17B37,
81R50,
17B70

Retrieve articles in all journals with MSC (1991): 17B37, 81R50, 17B70

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-97-03757-X

Received by editor(s):
August 31, 1995

Received by editor(s) in revised form:
December 11, 1995

Communicated by:
Roe Goodman

Article copyright:
© Copyright 1997
American Mathematical Society