2000 character limit reached
Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures (2404.01973v3)
Published 2 Apr 2024 in math.CO, math-ph, math.MP, and math.RT
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.
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