Corrigendum to "Generators of the Hecke algebra of (S_{2n},B_n)"

TL;DR

This paper addresses a correction to a previous work on the polynomial nature of structure constants in the Hecke algebra of a specific Gelfand pair, providing missing proof details through group action analysis.

Contribution

It supplies the missing argument in the proof that structure constants are polynomials in n for the Hecke algebra of (S_{2n}, B_n), clarifying the algebra's structure.

Findings

Confirmed polynomial nature of structure constants in the Hecke algebra

Provided detailed proof addressing previous gaps

Enhanced understanding of hyperoctahedral group actions

Abstract

In \cite{AC12}, among other things, we observed that the structure constants of the Hecke algebra of the Gel'fand pair $(S_{2n},B_n)$ are polynomials in $n$. It is brought to attention by Omar Tout that there is a missing argument in its proof. Here we provide the details of the missing argument by further analyzing various actions of the hyperoctahedral group.