A Clebsch-Gordan decomposition in positive characteristic

JOURNAL OF ALGEBRA

卷:560

Article

Donkin, Stephen^1,2  Martin, Samuel^1,2 

[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

[2] Earlham Inst, Norwich Res Pk, Norwich NR4 7UZ, Norfolk, England

关键词: Clebsch-Gordan;    Tilting modules;    Algebraic groups;    Representation theory;   

DOI  :  10.1016/j.jalgebra.2020.06.001

来源: Elsevier

【 摘 要 】

Let K be an algebraically closed field and G = SL2(K). Let E be the natural module and (SE)-E-r the rth symmetric power. We consider here, for r, s >= 0, the tensor product of (SE)-E-r and the dual of (SE)-E-s. In characteristic zero this tensor product decomposes according to the Clebsch-Gordan formula. We consider here the situation when K is a field of positive characteristic. We show that each indecomposable component occurs with multiplicity one and identify which modules occur for given r and s. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free