Quantum polynomial functors from $e$-Hecke pairs

Abstract

We define a new category of quantum polynomial functors extending the quantum polynomials introduced by Hong and Yacobi. We show that our category has many properties of the category of Hong and Yacobi and is the natural setting in which one can define composition of quantum polynomial functors. Throughout the paper we highlight several key differences between the theory of classical and quantum polynomial functors.

arXiv commentVersion 3: The title is changed from `Quantum polynomial functors from $e$-Hecke algebras' to `Quantum polynomial functors from $e$-Hecke pairs'! Several explanations are expanded and mistakes fixed, mostly in Section 6. We rephrased Theorem 6.11 (6.13 in v2) which was wrong as stated; we added Theorem 6.15