TILTING MODULES, DOMINANT DIMENSIONS AND BRAUER-SCHUR-WEYL DUALITY

In this paper we use the dominant dimension with respect to a tilting module to study the double centraliser property. We prove that if A is a quasi-hereditary algebra with a simple preserving duality and T is a faithful tilting A-module, then A has the double centralizer property with respect to T. This provides a simple and useful criterion which can be applied in many situations in algebraic Lie theory. We affirmatively answer a question of Mazorchuk and Stroppel by proving the existence of a unique minimal basic tilting module T over A for which A =End_EndA(T)(T). As an application, we establish a Schur-Weyl duality between the symplectic Schur algebra S^sy K (m, n) and the Brauer algebra B_n(−2m) on the space of dual partially harmonic tensors under certain condition.