仿射q-Schur代数S_(△)(2,3)的生成元与关系式  

The Generators and Relations for Affine q-Schur Algebra S_(Δ)(2,3)

作　　者：刘明强 杨倩 Mingqiang Liu;Qian Yang(Three Gorges Mathematical Research Center,China Three Gorges University,Yichang 443002,P.R.China)

机构地区：[1]三峡大学三峡数学研究中心,宜昌443002

出　　处：《数学学报(中文版)》2025年第1期113-125,共13页Acta Mathematica Sinica:Chinese Series

基　　金：宜昌市自然科学研究项目(A23-2-026)。

摘　　要：关于仿射q-Schur代数S_(Δ)(n,r)的生成元与关系式,Doty等人给出了n>r的表现,Deng-Du-Fu给出了仿射q-Schur代数S_(Δ)(r,r)的表现.当nΔ(n,r)的表现较复杂.本文从单项式基的角度,得到仿射q-Schur代数S_(Δ)(2,3)的一组单项式基,并给出仿射q-Schur代数S_(Δ)(2,3)一组新的生成元与关系式.In terms of the generators and relations of affine q-Schur algebra S_(Δ)(n,r),Doty et al.provided a presentation for n>r.Deng-Du-Fu gave the presentations for affine q-Schur algebra S_(Δ)(r,r).The presentation of the affine q-Schur algebra S_(Δ)(n,r)is more complicated in the case of n<r.In this paper,we obtain the monomial basis of affine q-Schur algebra S_(Δ)(2,3)and present a new set for generators and relations of q-Schur algebra S_(Δ)(2,3)by monomial basis.

关 键 词：仿射q-Schur代数 量子包络代数 单项式基 

分 类 号：O152.5[理学—数学]