Extensions of character formulas by the Littlewood decomposition

2016/12/12 by Mathias Pétréolle, Pétréolle, Mathias · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1612.03771

openalex publication_date 2016/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2015, the author proved combinatorially character formulas expressing sums of the (formal) dimensions of irreducible representations of symplectic groups, refining some works of Nekrasov and Okounkov, Han, King, and Westbury. In this article, we obtain generalizations of these character formulas, by using a bijection on integer partitions, namely the Littlewood decomposition, for which we prove new properties. As applications, we derive signed generating functions for subsets of integer partitions, and new hook length formulas.

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