Leading terms of relations for standard modules of affine Lie algebras $C_{n}\sp{(1)}$

TL;DR

This paper provides a combinatorial description of the leading terms in relations for standard modules of affine Lie algebra $C_{n}^{(1)}$, proposing new Rogers-Ramanujan type identities and connecting to Capparelli's identities.

Contribution

It introduces a novel combinatorial parametrization of relations for affine Lie algebra modules and conjectures new identities generalizing known Rogers-Ramanujan identities.

Findings

Parametrization of leading terms for affine Lie algebra modules

Conjectured Rogers-Ramanujan type identities for $n eq1$ and $k eq1$

Connection to Capparelli's identities for the case $n=k=1$

Abstract

In this paper we give a combinatorial parametrization of leading terms of defining relations for level $k$ standard modules for affine Lie algebra of type $C_{n}\sp{(1)}$. Using this parametrization we conjecture colored Rogers-Ramanujan type combinatorial identities for $n\geq 2$ and $k\geq 2$; the identity in the case $n=k=1$ is equivalent to one of Capparelli's identities.