Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type
Combinatorics
2018-03-08 v1 Number Theory
Quantum Algebra
Representation Theory
Abstract
We utilize the technique of staircases and jagged partitions to provide analytic sum-sides to some old and new partition identities of Rogers-Ramanujan type. Firstly, we conjecture a class of new partition identities related to the principally specialized characters of certain level modules for the affine Lie algebra . Secondly, we provide analytic sum-sides to some earlier conjectures of the authors. Next, we use these analytic sum-sides to discover a number of further generalizations. Lastly, we apply this technique to the well-known Capparelli identities and present analytic sum-sides which we believe to be new. All of the new conjectures presented in this article are supported by a strong mathematical evidence.
Keywords
Cite
@article{arxiv.1803.02515,
title = {Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type},
author = {Shashank Kanade and Matthew C. Russell},
journal= {arXiv preprint arXiv:1803.02515},
year = {2018}
}