Tight monomials for type B<sub>3

doi:10.1007/s11464-013-0342-6

Front Math Chin

2014, Vol. 9

Issue (1) : 213-238 https://doi.org/10.1007/s11464-013-0342-6

RESEARCH ARTICLE

Tight monomials for type B₃

Xiaoming WANG(

)

College of Information Technology, Shanghai Ocean University, Shanghai 201306, China

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Abstract

The global crystal basis or canonical basis plays an important role in the theory of the quantized enveloping algebras and their representations. The tight monomials are the simplest elements in the canonical basis. We discuss the tight monomials in quantized enveloping algebra of type B₃.

Keywords Quantized enveloping algebra canonical basis tight monomial

Corresponding Author(s): WANG Xiaoming,Email:xming.wang@yahoo.com

Issue Date: 01 February 2014

Cite this article:

Xiaoming WANG. Tight monomials for type B_{3[J]. Front Math Chin,
2014, 9(1): 213-238.}

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-013-0342-6
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I1/213

1	Caldero P, Marsh R, Morier-Genoud S. Realisation of Lusztig cones. Represent Theory , 2004, 8: 458-478 doi: 10.1090/S1088-4165-04-00225-0
2	Deng B, Du J. Tight monomials and the monomial basis property. J Algebra , 2010, 324: 458-478 doi: 10.1016/j.jalgebra.2010.09.022
3	Deng B, Du J, Parashall B, Wang J. Finite Dimensional Algebras and Quantum Groups. Mathematical Surveys and Monographs , Vol 150. Providence: Amer Math Soc, 2008 doi: 10.1090/surv/150
4	Hu Y, Ye J, Yue X. Canonical basis for type A₄—monomial elements. J Algebra , 2003, 263: 228-245 doi: 10.1016/S0021-8693(03)00066-8
5	Lusztig G. Canonical bases arising from quantized enveloping algebras. J Amer Math Soc , 1990, 3: 447-498 doi: 10.1090/S0894-0347-1990-1035415-6
6	Lusztig G. Quivers, perverse sheaves, and the quantized enveloping algebras. J Amer Math Soc , 1991, 4: 366-421 doi: 10.1090/S0894-0347-1991-1088333-2
7	Lusztig G. Tight monomials in quantized enveloping algebras. Israel Math Conf Proc , 1993, 7: 117-132
8	Lusztig G. Introduction to Quantum Groups. Boston: Birkh?user , 1993
9	Marsh R. More tight monomials in quantized enveloping algebras. J Algebra , 1998, 204: 711-732 doi: 10.1006/jabr.1997.7370
10	Reineke M. Monomials in canonical bases of quantum groups and quadratic forms. J Pure Appl Algebra , 2001, 157: 301-309 doi: 10.1016/S0022-4049(00)00008-6
11	Wang X. Tight monomials for type G₂ and A₃.Comm Algebra , 2010, 38: 3597-3615 doi: 10.1080/00927870903200919
12	Wang X. Tight monomials for quantum enveloping algebras of rank-2 Kac-Moody Lie algebras. J Pure Appl Algebra , 2012, 216: 694-708 doi: 10.1016/j.jpaa.2011.08.005
13	Xi N. Canonical basis for type B₂.J Algebra , 1999, 214: 8-21 doi: 10.1006/jabr.1998.7688
14	Xi N. Canonical basis for type A₃.Comm Algebra , 1999, 27: 5703-5710 doi: 10.1080/00927879908826784

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