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

Year 2015, Volume: 17 Issue: 17, 105 - 138, 01.06.2015

C. Bowman S. R. Doty S. Martin

https://doi.org/10.24330/ieja.266215

Cited By: 5

Abstract

We study the structure of the indecomposable direct summands of tensor products
of two restricted rational simple modules for the algebraic group SL3(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