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On Schur algebras and related algebras III: integral representations

Published online by Cambridge University Press:  24 October 2008

Stephen Donkin
Stephen Donkin
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS
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Extract

Let G be a reductive group over an algebraically closed field K. In [8] and [9] we defined and studied certain finite dimensional K-algebras SK(π), associated to G via a finite saturated set π of dominant weights. The algebras are defined over ℤ, i.e. SK(π) = K ⊗ℤSℤ(π) for an order Sℤ(π) of Sℚ(π), and if G is a general linear group or a Chevalley group then the order Sℤ(π) arises naturally from the corresponding group scheme G over ℤ (or Kostant ℤ-form Uℤ). These algebras may be regarded as (and were obtained as) direct generalizations of the Schur algebras S(n, r) studied by Green in [10].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 1 , July 1994 , pp. 37 - 55
Copyright
Copyright © Cambridge Philosophical Society 1994

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