DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3: THE p ≥ 5 CASE

Authors : C Bowman, S R Doty, S Martin

Pages : 105-138

Doi:10.24330/ieja.266215

View : 23 | Download : 12

Publication Date : 2015-06-01

Article Type : Research Paper

Abstract :We study the structure of the indecomposable direct summands of tensor products of two restricted rational simple modules for the algebraic group SL3insert ignore into journalissuearticles values(K);, where K is an algebraically closed field of characteristic p ≥ 5. We also give a characteristic-free algorithm for the decomposition of such a tensor product into indecomposable direct summands. The p < 5 case was studied in the authors’ earlier paper [4]. We find that for characteristics p ≥ 5 all the indecomposable summands are rigid, in contrast to the characteristic 3 case.
Keywords : Algebraic groups, tilting modules, Weyl modules, quivers