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arXiv · 2607.06927

A categorification of the Brenti--Welker identity

Deke Zhao·Zhankui Xiao
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Abstract

The paper aims to provide a categorification of the Brenti--Welker identity involving Eulerian numbers in (Adv. Appl. Math. 42 (2009): 545--556) by lifting it from an enumerative equality to an isomorphism of symmetric group representations. To do so, we study the decomposition of the tensor product of $(\mathbb{C}^r)^{\otimes n}$ and modules affording Foulkes characters as modules of the symmetric group. The main ingredient of the proof is a combinatorial identity which may be of independent interest.

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BibTeXRIS

Deke Zhao, Zhankui Xiao. 2026-07-08. A categorification of the Brenti--Welker identity. https://doi.org/10.1016/j.aam.2026.103048

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