## Pétréolle, Mathias - A Nekrasov-Okounkov type formula for affine $\widetilde{C}$

dmtcs:2498 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
A Nekrasov-Okounkov type formula for affine $\widetilde{C}$

Authors: Pétréolle, Mathias

In 2008, Han rediscovered an expansion of powers of Dedekind $\eta$ function due to Nekrasov and Okounkov by using Macdonald's identity in type $\widetilde{A}$. In this paper, we obtain new combinatorial expansions of powers of $\eta$, in terms of partition hook lengths, by using Macdonald's identity in type $\widetilde{C}$ and a new bijection. As applications, we derive a symplectic hook formula and a relation between Macdonald's identities in types $\widetilde{C}$, $\widetilde{B}$, and $\widetilde{BC}$.

Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: Macdonald’s identities,Dedekind $\eta$ function,affine root systems,integer partitions,t-cores,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]