Endsk(2,5)(Ω5k)与Enduk(2,5)(Ω5k)的结构

On the Structure of Endsk(2,5)(Ω5k) and Enduk(2,5)(Ω5k)

摘要:

利用张量空间Ω5k作为glk(2)量子包络代数(qSchur代数)的tilting模分解以及在n=2时已知的tilting模结构，给出Ω5k作为无穷小qSchur代数及小qSchur代数的模时 Endsk(2,5)(Ω5k)与Enduk(2,5)(Ω5k) 的维数、一组生成元以及主模分解.

关键词:无穷小qSchur代数; 小qSchur代数; SchurWeyl对偶

Abstract:

By using the fact that tensor space Ω5k can be written as a direct sum of tilting modules for the quantum enveloping algebra (qSchur algebra) of glk(2) and the structure of tilting modules for n=2, we will determine the dimension, a set of generators and the decomposition of principal modules of Endsk(2,5)(Ω5k) and Enduk(2,5)(Ω5k), when Ω5k is considered as a module of the infinitesimal qSchur algebra and the little qSchur algebra.

Key words:infinitesimal qSchur algebra; little qSchur algebra; SchurWeyl duality