THE $q$ -SCHUR ALGEBRAS AND $q$ -SCHUR DUALITIES OF FINITE TYPE
THE $q$ -SCHUR ALGEBRAS AND $q$ -SCHUR DUALITIES OF FINITE TYPE
复制标题
DOI：
10.1017/s1474748020000031
复制
发表时间：
2017-10
影响因子：
0.9
通讯作者：
Lipeng Luo;Weiqiang Wang
中科院分区：
文献类型：
--
作者：
Lipeng Luo;Weiqiang Wang
Abstract We formulate a $q$ -Schur algebra associated with an arbitrary $W$ -invariant finite set $X_{\text{f}}$ of integral weights for a complex simple Lie algebra with Weyl group $W$ . We establish a $q$ -Schur duality between the $q$ -Schur algebra and Hecke algebra associated with $W$ . We then realize geometrically the $q$ -Schur algebra and duality and construct a canonical basis for the $q$ -Schur algebra with positivity. With suitable choices of $X_{\text{f}}$ in classical types, we recover the $q$ -Schur algebras in the literature. Our $q$ -Schur algebras are closely related to the category ${\mathcal{O}}$ , where the type $G_{2}$ is studied in detail.
