Can I read Remarks on the conjectures of Capparelli, Meurman, Primc and Primc on EtoBox?

Remarks on the conjectures of Capparelli, Meurman, Primc and Primc by Kanade, Shashank; Russell, Matthew C.; Tsuchioka, Shunsuke; Warnaar, S. Ole is a scholarly article available to read on EtoBox.

What is Remarks on the conjectures of Capparelli, Meurman, Primc and Primc about?

In a sequence of two papers, S. Capparelli, A. Meurman, A. Primc, M. Primc (CMPP) and then M. Primc put forth three remarkable sets of conjectures, stating that the generating functions of coloured integer partition in which the parts satisfy restrictions on the multiplicities admit simple infinite product forms. While CMPP related one set of conjectures to the principally specialised characters of standard modules for the affine Lie algebra $\mathrm{C}_n^{(1)}$, finding a Lie-algebraic interpretation for the remaining two sets remained an open problem. In this paper, we use the work of Griffin, Ono and the fourth author on Rogers-Ramanujan identities for affine Lie algebras to solve this problem, relating the remaining two sets of conjectures to non-standard specialisations of standard modules for $\mathrm{A}_{2n}^{(2)}$ and $\mathrm{D}_{n+1}^{(2)}$. We also use their work to formulate conjectures for the bivariate generating function of one-parameter families of CMPP partitions in terms of Hall-Littlewood symmetric functions. We make a detailed study of several further aspects of CMPP partitions, obtaining (i) functional equations for bivariate generating functions which generali

Author

Kanade, Shashank; Russell, Matthew C.; Tsuchioka, Shunsuke; Warnaar, S. Ole

Published

2024

Language

EN