A note on degenerate cyclotomic Yokonuma-Hecke algebras

TL;DR

This paper proves the cellularity of degenerate cyclotomic Yokonuma-Hecke algebras and develops a fusion procedure to explicitly construct primitive idempotents, advancing their algebraic understanding.

Contribution

It introduces the first explicit cellular basis for these algebras and establishes a fusion procedure for primitive idempotents.

Findings

Established cellularity of $Y_{r,n}^{d}$

Constructed explicit cellular basis

Developed fusion procedure for primitive idempotents

Abstract

In this note, we first prove that the degenerate cyclotomic Yokonuma-Hecke algebra $Y_{r,n}^{d}$ is cellular by constructing an explicit cellular basis. We then develop the fusion procedure for $Y_{r,n}^{d}$, that is, a complete set of pairwise orthogonal primitive idempotents for $Y_{r,n}^{d}$ is defined by consecutive evaluations of a certain rational function.