Séminaire Lotharingien de Combinatoire, B81c (2020), 28 pp.

Adam Walsh and S. Ole Warnaar

Modular Nekrasov-Okounkov Formulas

Abstract. Using Littlewood's map, which decomposes a partition into its r-core and r-quotient, Han and Ji have shown that many well-known hook-length formulas admit modular analogues. In this paper we present a variant of the Han-Ji `multiplication theorem' based on a new analogue of Littlewood's decomposition. We discuss several applications to hook-length formulas, one of which leads us to conjecture a modular analogue of the q,t-Nekrasov-Okounkov formula.

Received: February 17, 2019. Accepted: February 13, 2020.

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