Parafermionic derivation of Andrews-type multiple sums

TL;DR

This paper derives a multi-parafermion basis for Z_k parafermionic models, constructs its generating function, and connects it to Andrews multiple-sums, providing new insights into partition enumeration and fermionic characters.

Contribution

It introduces a new basis for parafermionic models and links it to Andrews multiple-sums, offering novel expressions for graded parafermion characters.

Findings

Derived a multi-parafermion basis for Z_k models

Constructed generating functions matching Andrews sums

Provided new expressions for graded parafermion characters

Abstract

A multi-parafermion basis of states for the Z_k parafermionic models is derived. Its generating function is constructed by elementary steps. It corresponds to the Andrews multiple-sum which enumerates partitions whose parts separated by the distance k-1 differ by at least 2. Two analogous bases are derived for graded parafermions; one of these entails a new expression for their fermionic characters.