POLYNOMIAL FUNCTORS AND TWO-PARAMETER QUANTUM SYMMETRIC PAIRS

Abstract

We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) polynomial functors give a new interpretation of polynomial representations of the general linear groups GL(n), the two-parameter polynomial functors give a new interpretation of (polynomial) representations of the quantum symmetric pair (U-Q,q(B)(gl(n)), U-q(gl(n))) which specializes to type AIII/AIV quantum symmetric pairs. The coideal subalgebra U-Q,q(B) (gl(n)) appears in a Schur-Weyl duality with the type B Hecke algebra H-Q,q(B) (d). We endow two-parameter polynomial functors with a cylinder braided structure which we use to construct the two-parameter Schur functors. Our polynomial functors can be precomposed with the quantum polynomial functors of type A producing new examples of action pairs.