Classical theta functions from a quantum group perspective

TL;DR

This paper constructs a quantum group at roots of unity to model classical theta functions and their symmetries, providing a new algebraic perspective on abelian Chern-Simons theory.

Contribution

It introduces a quantum group framework at roots of unity for classical theta functions, linking quantum algebra with topological quantum field theory.

Findings

Quantum group at roots of unity models classical theta functions

Heisenberg and modular group actions are represented algebraically

Provides a new perspective on abelian Chern-Simons theory

Abstract

In this paper we construct the quantum group, at roots of unity, of abelian Chern-Simons theory. We then use it to model classical theta functions and the actions of the Heisenberg and modular groups on them.