The Quantum Pair of Pants

TL;DR

This paper analyzes the spectrum of a multiplication operator on a Hilbert space of holomorphic functions with two holes and characterizes the associated $C^*$-algebra, termed the quantum pair of pants.

Contribution

It introduces the quantum pair of pants as a new $C^*$-algebra generated by a specific multiplication operator on a multiply connected domain.

Findings

Computed the spectrum of the multiplication operator.

Determined the structure of the generated $C^*$-algebra.

Established the algebra as the quantum pair of pants.

Abstract

We compute the spectrum of the operator of multiplication by the complex coordinate in a Hilbert space of holomorphic functions on a disk with two circular holes. Additionally we determine the structure of the $C^*$-algebra generated by that operator. The algebra can be considered as the quantum pair of pants.