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Finite dimensional representations of $U_{q}(sl(2,1))$

Author(s): Yi Ming Zou
Journal: Proc. Amer. Math. Soc. 125 (1997), 1607-1616.
MSC (1991): Primary 17B37; Secondary 81R50, 17B70
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Abstract: Structures of the finite dimensional simple weight $U_{q}(sl(2,1))$-modules are studied in detail for both the generic and the roots of 1 cases.

References:

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, $q$-Oscillator realizations of the quantum superalgebras $sl_{q}(m,n)$ and $osp_{q}(m,2n)$, Commun. Math. Phys. 137 (1991), 149-160. MR 92a:81075

4.
M. D. Gould and M. Scheunert, Classification of finite dimensional unitary irreps for $U[gl(m/n)]$, 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 $q$ 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 $q$ and link polynomials, J. Math. Phys. 33 (11) (1992), 3918-3930. MR 94d:20040

13.
R. B. Zhang, Finite-dimensional representations of $U_{q}(osp(1/2n))$ and its connection with quantum $so(2n+1)$, Lett. Math. Phys. 25 (1992), 317-325. MR 93k:17042

14.
Y. M. Zou, Deformations of enveloping algebra of Lie superalgebra $sl(m,n)$, Commun. Math. Phys. 162 (3) (1994), 467-479. MR 95h:17014

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Additional Information:

DOI: 10.1090/S0002-9939-97-03757-X
PII: S 0002-9939(97)03757-X
Received by editor(s): August 31, 1995
Received by editor(s) in revised form: December 11, 1995
Communicated by: Roe Goodman
Copyright of article: Copyright 1997, American Mathematical Society

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