The quantum general linear supergroup, canonical bases and Kazhdan-Lusztig polynomials

作     者：ZHANG HeChun Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China 

作者机构：Department of Mathematical Sciences Tsinghua University Beijing China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2009年第52卷第3期

页      面：401-416页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No. 10471070) 

主　　题：canonical basis crystal basis Kazhdan-Lusztig polynomial 

摘      要：Canonical bases of the tensor powers of the natural Uq(glm|n)-module V are constructed by adapting the work of Frenkel, Khovanov and Kirrilov to the quantum supergroup setting. This result is generalized in several directions. We first construct the canonical bases of the Z2-graded symmetric algebra of V and tensor powers of this superalgebra; then construct canonical bases for the superalgebra Oq(Mm|n) of a quantum (m, n) × (m, n)-supermatrix; and finally deduce from the latter result the canonical basis of every irreducible tensor module for Uq(glm|n) by applying a quantum analogue of the Borel-Weil construction.