On Schur algebras and related algebras III: integral representations
Copyright policy )On Schur algebras and related algebras III: integral representations
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].
- Queen Mary University of London United Kingdom
Representation theory for linear algebraic groups, general linear group schemes, reductive groups, projective modules, induced modules, Modular representations and characters, symmetric groups, Representations of finite symmetric groups, hyperalgebras, dominant weights, generalized Schur algebras, Combinatorial aspects of representation theory, Integral representations of infinite groups, Weyl filtrations over Dedekind domains
Representation theory for linear algebraic groups, general linear group schemes, reductive groups, projective modules, induced modules, Modular representations and characters, symmetric groups, Representations of finite symmetric groups, hyperalgebras, dominant weights, generalized Schur algebras, Combinatorial aspects of representation theory, Integral representations of infinite groups, Weyl filtrations over Dedekind domains
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