The q-Weyl group of a q-Schur algebra
The q-Weyl group of a q-Schur algebra
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发表时间：
1999-02
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通讯作者：
Pierre Baumann
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作者：
Pierre Baumann
Dipper和James的q-Schur代数是Drinfeld和Jimbo的量子化包络代数U_q（gl_m）的商。U_q（gl_m）的q-Weyl群（也称为Lusztig自同构辫群）引出了q-Schur代数的一组内自同构。我们精确地描述了定义这些内自同构的q-Schur代数中的元素。这种描述使我们能够恢复q-Weyl群的某些已知性质。
The q-Schur algebras of Dipper and James are quotients of the quantized enveloping algebras U_q(gl_m) of Drinfeld and Jimbo. The q-Weyl group of U_q(gl_m) (also known as Lusztig's automorphisms braid group) induces a group of inner automorphisms of the q-Schur algebras. We describe precisely elements in the q-Schur algebras that define these inner automorphisms. This description allows us to recover certain known properties of the q-Weyl group.