Quantum Polynomial Functors

Jiuzu Hong, Oded Yacobi

Abstract

We construct a category of quantum polynomial functors which deforms Friedlander and Suslin's category of strict polynomial functors. The aim of this paper is to develop the basic structural properties of this category. We construct quantum Schur and Weyl functors and show that quantum divided powers form projective generators for the category of quantum polynomial functors of degree $d$. Using this result we prove that the category of quantum polynomial functors is braided, and give a new and streamlined proof of quantum $(GL(m),GL(n))$ duality, along with other results in quantum invariant theory.