New Partition Identities From $C_{\ell}^{(1)}$-Modules

TL;DR

This paper proposes new combinatorial partition identities inspired by affine Lie algebra representations and explores their potential connections beyond established theoretical frameworks.

Contribution

It introduces novel Rogers-Ramanujan type colored partition identities linked to affine Lie algebra modules and conjectures additional identities without direct ties to representation theory.

Findings

Conjectured new partition identities related to $C_{ ext{ell}}^{(1)}$-modules.

Identified potential combinatorial structures beyond affine Lie algebra connections.

Proposed conjectures open avenues for further mathematical exploration.

Abstract

In this paper we conjecture combinatorial Rogers-Ramanujan type colored partition identities related to standard representations of the affine Lie algebra of type $C^{(1)}_\ell$, $\ell\geq2$, and we conjecture similar colored partition identities with no obvious connection to representation theory of affine Lie algebras.