A categorification of the Brenti--Welker identity

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.