Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures

Fuente: arXiv
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Autor principal: Yang, Chenglang
Formato: Preprint
Publicado: 2024
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author Yang, Chenglang
author_facet Yang, Chenglang
contents The symplectic/orthogonal contents of partitions are related to the dimensions of irreducible representations of symplectic/orthogonal groups. In 2012, motivated by Nekrasov--Okounkov's hook-length formula and Stanley's hook-content formula, Amdeberhan proposed several conjectures about infinite product formulas for certain generating functions of hook-lengths and symplectic/orthogonal contents. Some special cases of his conjectures were recently proved by Amdeberhan, Andrews and Ballantine. In this paper, we prove the general cases of Amdeberhan's conjectures.
format Preprint
id arxiv_https___arxiv_org_abs_2404_01973
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures
Yang, Chenglang
Combinatorics
Mathematical Physics
Representation Theory
The symplectic/orthogonal contents of partitions are related to the dimensions of irreducible representations of symplectic/orthogonal groups. In 2012, motivated by Nekrasov--Okounkov's hook-length formula and Stanley's hook-content formula, Amdeberhan proposed several conjectures about infinite product formulas for certain generating functions of hook-lengths and symplectic/orthogonal contents. Some special cases of his conjectures were recently proved by Amdeberhan, Andrews and Ballantine. In this paper, we prove the general cases of Amdeberhan's conjectures.
title Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures
topic Combinatorics
Mathematical Physics
Representation Theory
url https://arxiv.org/abs/2404.01973