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On the blocks of semisimple algebraic groups and associated generalized Schur algebras

De Visscher, M. (2008). On the blocks of semisimple algebraic groups and associated generalized Schur algebras. Journal of Algebra, 319(3), pp. 952-965. doi: 10.1016/j.jalgebra.2007.11.015

Abstract

In this paper we give a new proof for the description of the blocks of any semisimple simply connected algebraic group when the characteristic of the field is greater than 5. The first proof was given by Donkin and works in arbitrary characteristic. Our new proof has two advantages. First we obtain a bound on the length of a minimum chain linking two weights in the same block. Second we obtain a sufficient condition on saturated subsets π of the set of dominant weights which ensures that the blocks of the associated generalized Schur algebra are simply the intersection of the blocks of the algebraic group with the set π. However, we show that this is not the case in general for the symplectic Schur algebras, disproving a conjecture of Renner.

Publication Type: Article
Publisher Keywords: blocks, semisimple algebraic groups, Schur algebras, MODULES, REPRESENTATIONS
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/968
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