Quantum polynomial functors from $e$-Hecke pairs

TL;DR

This paper introduces a new category of quantum polynomial functors that extends previous work, enabling composition and highlighting differences from classical polynomial functors.

Contribution

It defines a novel category of quantum polynomial functors based on $e$-Hecke pairs, expanding the theoretical framework and compositional capabilities.

Findings

The new category shares many properties with Hong and Yacobi's quantum polynomials.

It provides a natural setting for defining composition of quantum polynomial functors.

Key differences between classical and quantum polynomial functors are emphasized.

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.