Lowering operators, orthogonal decomposition of tensor space, and quantized Schur--Weyl duality

Stephen Doty, Anthony Giaquinto, Stuart Martin

For $q$ generic, Jimbo showed that $q$-tensor space $V_q^{\otimes r}$ (where $V_q$ is the $n$-dimensional vector representation) satisfies Schur--Weyl duality with respect to the c…