Crystal bases for
Author:
Yi Ming Zou
Journal:
Proc. Amer. Math. Soc. 127 (1999), 22132223
MSC (1991):
Primary 17B37; Secondary 81R59, 17B70
Published electronically:
March 23, 1999
MathSciNet review:
1486756
Fulltext PDF Free Access
Abstract 
References 
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Abstract: A construction of the crystal bases for the quantized enveloping algebra of is discussed.
 1.
V.
G. Drinfel′d, Quantum groups, (Berkeley, Calif., 1986)
Amer. Math. Soc., Providence, RI, 1987, pp. 798–820. MR 934283
(89f:17017)
 2.
R. Floreanini, D. A. Leites, and L. Vinet, On the defining relations of quantum superalgebras, Lett. Math. Phys. 23 (1991), 127131.
 3.
R. Floreanini, V. P. Spiridonov, and L. Vinet, Oscillator realizations of the quantum superalgebras and , Commun. Math. Phys. 137 (1991), 149160.
 4.
M. Jimbo, A difference analog of and the YangBaxter equation, Lett. Math. Phys. 10 (1985), 6369.
 5.
V.
G. Kac, Lie superalgebras, Advances in Math.
26 (1977), no. 1, 8–96. MR 0486011
(58 #5803)
 6.
V.
Kac, Representations of classical Lie superalgebras,
Differential geometrical methods in mathematical physics, II (Proc. Conf.,
Univ. Bonn, Bonn, 1977), Lecture Notes in Math., vol. 676, Springer,
Berlin, 1978, pp. 597–626. MR 519631
(80f:17006)
 7.
Masaki
Kashiwara, Crystalizing the 𝑞analogue of universal
enveloping algebras, Comm. Math. Phys. 133 (1990),
no. 2, 249–260. MR 1090425
(92b:17018)
 8.
M.
Kashiwara, On crystal bases of the 𝑄analogue of universal
enveloping algebras, Duke Math. J. 63 (1991),
no. 2, 465–516. MR 1115118
(93b:17045), http://dx.doi.org/10.1215/S0012709491063210
 9.
Yi
Ming Zou, Finitedimensional representations of
𝑈_{𝑞}(𝑠𝑙(2,1)), Proc. Amer. Math. Soc. 125 (1997), no. 6, 1607–1616. MR 1371148
(97g:17019), http://dx.doi.org/10.1090/S000299399703757X
 1.
 V. G. Drinfeld, Quantum groups, Proc. Int. Cong. Math., Berkeley, vol. I, 1986, pp. 789820. MR 89f:17017
 2.
 R. Floreanini, D. A. Leites, and L. Vinet, On the defining relations of quantum superalgebras, Lett. Math. Phys. 23 (1991), 127131.
 3.
 R. Floreanini, V. P. Spiridonov, and L. Vinet, Oscillator realizations of the quantum superalgebras and , Commun. Math. Phys. 137 (1991), 149160.
 4.
 M. Jimbo, A difference analog of and the YangBaxter equation, Lett. Math. Phys. 10 (1985), 6369.
 5.
 V. Kac, Lie superalgebras, Adv. Math. 26 (1977), 896. MR 58:5803
 6.
 , Representations of classical Lie superalgebras, Lecture Notes in Math., vol. 676, 1977, pp. 579626. MR 80f:17006
 7.
 M. Kashiwara, Crystalizing the analogue of universal enveloping algebras, Commun. Math. Phys. 133 (1990), 249260. MR 92b:17018
 8.
 , On crystal bases of the analogue of universal enveloping algebras, Duke Math. J. 63 (2) (1991), 465516. MR 93b:17045
 9.
 Y. M. Zou, Finite dimensional representations of , Proc. of AMS 125(6) (1997), 16071616. MR 97g:17019
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Additional Information
Yi Ming Zou
Affiliation:
Department of Mathematical Sciences, University of WisconsinMilwaukee, Milwaukee, Wisconsin 53201
Email:
ymzou@csd.uwm.edu
DOI:
http://dx.doi.org/10.1090/S0002993999048212
PII:
S 00029939(99)048212
Received by editor(s):
February 21, 1997
Received by editor(s) in revised form:
October 20, 1997
Published electronically:
March 23, 1999
Communicated by:
Roe Goodman
Article copyright:
© Copyright 1999 American Mathematical Society
