Linkage and translation for tensor products

Abstract

Let G be a simple algebraic group over an algebraically closed field of characteristic p>0. The decomposition into blocks of the category of finite-dimensional rational G-modules is described by two classical results of H.H. Andersen and J.C. Jantzen: The linkage principle and the translation principle. We will start by recalling these results and explaining why they are a-priori not well suited for studying tensor products of G-modules. Then we introduce a tensor ideal of 'singular G-modules' and give a linkage principle and a translation principle for tensor products in the corresponding quotient category. This also gives rise to a decomposition of the quotient category as an external tensor product of its principal block with the Verlinde category of G.

Speaker

Research Project:

Quantum Symmetric Pairs and Total Positivity