Generalizations of the Andrews-Bressoud Identities for the $N=1$ Superconformal Model $SM(2,4\nu)$

TL;DR

This paper generalizes Rogers-Ramanujan identities to relate fermionic and bosonic character forms of the superconformal model SM(2,4 u), revealing an infinite family of fermionic series for each bosonic form.

Contribution

It introduces new generalized identities connecting fermionic and bosonic characters in superconformal models, expanding the understanding of their mathematical structure.

Findings

Infinite family of fermionic q-series for each bosonic character

Unified framework for superconformal model characters

Extension of Rogers-Ramanujan identities to superconformal models

Abstract

We present generalized Rogers-Ramanujan identities which relate the fermi and bose forms of all the characters of the superconformal model $SM(2,4\nu).$ In particular we show that to each bosonic form of the character there is an infinite family of distinct fermionic $q-$ series representations.