Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures
Combinatorics
2025-02-18 v3 Mathematical Physics
math.MP
Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2404.01973,
title = {Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures},
author = {Chenglang Yang},
journal= {arXiv preprint arXiv:2404.01973},
year = {2025}
}
Comments
18 pages, accepted for publication in Proceedings of the London Mathematical Society