Let be a commutative ring with and an invertible element of . The (specialized) quantum group over of the general linear group acts on mixed tensor space , where denotes the natural -module , and are nonnegative integers and is the dual -module to . The image of in is called the rational -Schur algebra . We construct a bideterminant basis of . There is an action of a -deformation of the walled Brauer algebra on mixed tensor space centralizing the action of . We show that . By a previous result, the image of in is . Thus, a mixed tensor space as -bimodule satisfies Schur–Weyl duality.
"Quantized mixed tensor space and Schur–Weyl duality." Algebra Number Theory 7 (5) 1121 - 1146, 2013. https://doi.org/10.2140/ant.2013.7.1121