|
Crystal bases for
Author(s):
Yi Ming
Zou
Journal:
Trans. Amer. Math. Soc.
353
(2001),
3789-3802.
MSC (2000):
Primary 16W30, 16S80, 22E70
Posted:
May 3, 2001
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We construct crystal bases for certain infinite dimensional representations of the -deformation of the Lie superalgebra .
References:
-
- 1.
- G. Benkart, S.-J. Kang and M. Kashiwara, Crystal Bases for the quantum superalgebra
, J. of Amer. Math. Soc. 13(2) (2000), 295-331. MR 2000m:17015 - 2.
- J. C. Jantzen, Lectures on Quantum Groups, Graduate Studies in Mathematics, vol. 6, AMS, 1995. MR 96m:17029
- 3.
- A. Joseph, Quantum Groups and Their Primitive Ideals, Ergebnisse der Mathematik (3) 29, Springer-Verlag, Berlin, 1995. MR 96d:17015
- 4.
- V. Kac, Lie superalgebras, Adv. Math. 26 (1977), 8-96. MR 58:5803
- 5.
- -, Representations of classical Lie superalgebras, Lecture Notes in Math., vol. 676, Springer, Berlin, 1978, pp. 597-626. MR 80f:17006
- 6.
- M. Kashiwara, Crystalizing the
-analogue of universal enveloping algebras, Commun. Math. Phys. 133 (1990), 249-260. MR 92b:17018 - 7.
- -, On crystal bases of the
-analogue of universal enveloping algebras, Duke Math. J. 63(2) (1991), 465-516. MR 93b:17045 - 8.
- -, Crystal base and Littelmann's refined Demazure character formula, Duke Math. J. 71 (1993), 839-858. MR 95b:17019
- 9.
- -, On crystal bases, Representations of Groups, CMS conference Proc., vol. 16, AMS, 1995, pp. 155-197. MR 97a:17016
- 10.
- M. Kashiwara and T. Nakashima, Crystal graphs for representations of the
-analogue of classical Lie algebras, J. of Algebra 165 (1994), 295-345. MR 95c:17025 - 11.
- I. M. Musson and Y. M. Zou, Crystal bases for
, J. of Algebra 210 (1998), 514-534. MR 99j:17024 - 12.
- Y. M. Zou, Finite-dimensional representations of
, J. Algebra 169(3) (1994), 827-846. MR 95j:17005 - 13.
- -, Deformation of the universal enveloping algebra of
, Canad. Math. Bull. 39(4) (1996), 499-506. MR 97m:17021 - 14.
- -, Crystal bases for
, Proc. of Amer. Math. Soc. 127(8) (1999), 2213-2223. MR 99j:17028
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(2000):
16W30, 16S80, 22E70
Retrieve articles in all Journals with MSC
(2000):
16W30, 16S80, 22E70
Additional Information:
Yi Ming
Zou
Affiliation:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201
Email:
ymzou@uwm.edu
DOI:
10.1090/S0002-9947-01-02842-2
PII:
S 0002-9947(01)02842-2
Received by editor(s):
February 26, 1999
Received by editor(s) in revised form:
January 30, 2001
Posted:
May 3, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
|