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Linkage and translation for tensor products

来源: 05-12

时间:Friday, 10:30-11:30 am May 12, 2023

地点:Ning Zhai W11

组织者:Will Donovan, Penghui Li, Peng Shan, Changjian Su

主讲人:Jonathan Gruber, Research Fellow National University of Singapore

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


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