Algebra Seminar

In 1990, J. A. Green investigated certain subalgebras, called Borel subalgebras, of the Schur algebra associated with the Borel subgroups of the general linear group. Besides their combinatorial definition, these algebras are quasi-hereditary and give rise to a triangular decomposition of the Schur algebra with which Weyl and co-Weyl modules can be described as induced modules by using tensor and hom functors. Part of Green's work has been generalized to the q-Schur algebra by Parshall and Wang.

In this talk, we will look at the generalization of Green's work to a series of q-Schur type algebras, called q-Schur^m algebras, which is a subclass of cyclotomic q-Schur algebras. In particular, we will prove that a Borel type subalgebra of the q-Schur^m algebra of degree (n,r) is isomorphic to a Borel subalgebra of the q-Schur algebra of degree (mn,r).