The modular representation theory ofq-Schur algebras. II
Copyright policy )The modular representation theory ofq-Schur algebras. II
A Brauer-type homomorphism is constructed for the q-Schur algebra and its kernel is described explicitly. We also prove that the \(q\)-Schur algebra corresponding to the symmetric group on \(ml\) letters modulo an appropriate ideal is isomorphic to the Schur algebra corresponding to the symmetric group on m letters. Finally, we prove that the pull-back of an irreducible representation through the Brauer homomorphism remains irreducible as a q-Schur algebra module. This is a \(q\)-analogue of some fundamental result in the modular representation theory, which was proved by Leonard Scott in 1973.
- University of Sydney Australia
- DigiZeitschriften Germany
Representation theory for linear algebraic groups, pull-back, Representations of orders, lattices, algebras over commutative rings, Modular representations and characters, Representations of finite symmetric groups, irreducible representation, Endomorphism rings; matrix rings, Article, symmetric group, q-Schur algebra module, 510.mathematics, kernel, Brauer homomorphism, q-Schur algebra, Group rings of finite groups and their modules (group-theoretic aspects)
Representation theory for linear algebraic groups, pull-back, Representations of orders, lattices, algebras over commutative rings, Modular representations and characters, Representations of finite symmetric groups, irreducible representation, Endomorphism rings; matrix rings, Article, symmetric group, q-Schur algebra module, 510.mathematics, kernel, Brauer homomorphism, q-Schur algebra, Group rings of finite groups and their modules (group-theoretic aspects)
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