# Decomposition of tensor products of modular irreducible representations for SL3

Bowman, Christopher, Doty, S., Martin, S. (2011) Decomposition of tensor products of modular irreducible representations for SL3. International Electronic Journal of Algebra, 9 . pp. 177-219. E-ISSN 1306-6048. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:70137)

 The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. Official URLhttp://www.ieja.net/files/papers/volume-9/Volume-8...

## Abstract

We give an algorithm for working out the indecomposable direct

summands in a Krull–Schmidt decomposition of a tensor product of two simple

modules for G = SL3 in characteristics 2 and 3. It is shown that there is a

finite family of modules such that every such indecomposable summand is

expressible as a twisted tensor product of members of that family.

Along the way we obtain the submodule structure of various Weyl and

tilting modules. Some of the tilting modules that turn up in characteristic

3 are not rigid; these seem to provide the first example of non-rigid tilting

modules for algebraic groups. These non-rigid tilting modules lead to examples

of non-rigid projective indecomposable modules for Schur algebras, as shown

in the Appendix.

Higher characteristics (for SL3) will be considered in a later paper.

Item Type: Article Algebraic groups, tilting modules, Weyl modules, quivers Q Science > QA Mathematics (inc Computing science) Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Christopher Bowman 16 Nov 2018 12:01 UTC 16 Nov 2021 10:25 UTC https://kar.kent.ac.uk/id/eprint/70137 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-6046-8930