Archiv der Mathematik

, Volume 92, Issue 3, pp 206–214 | Cite as

Hook modules for general linear groups

  • Stephen Doty
  • Stuart Martin


For an arbitrary infinite field k of characteristic p > 0, we describe the structure of a block of the algebraic monoid M n (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 GL n (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.

Mathematics Subject Classification (2000).

Primary 20G05 Secondary 20C30 


Weyl modules Schur algebras symmetric groups 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Stephen Doty
    • 1
  • Stuart Martin
    • 2
  1. 1.Mathematics and StatisticsLoyola University ChicagoChicagoUSA
  2. 2.Magdalene CollegeCambridgeUnited Kingdom

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