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- Title
Hook modules for general linear groups.
- Authors
Stephen Doty; Stuart Martin
- Abstract
Abstract. For an arbitrary infinite field k of characteristic p > 0, we describe the structure of a block of the algebraic monoid Mn(k) (all n × n matrices over k), or, equivalently, a block of the Schur algebra S(n, p), whose simple modules are indexed by p-hook partitions. The result is known; we give an elementary and self-contained proof, based only on a result of Peel and Donkin’s description of the blocks of Schur algebras. The result leads to a character formula for certain simple GLn(k)-modules, valid for all n and all p. This character formula is a special case of one found by Brundan, Kleshchev, and Suprunenko and, independently, by Mathieu and Papadopoulo.
- Subjects
MODULES (Algebra); GROUP theory; MONOIDS; LATTICE theory; MATHEMATICAL analysis
- Publication
Archiv der Mathematik, 2009, Vol 92, Issue 3, p206
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-009-2789-y