Cell structures for the Yokonuma-Hecke algebra and the algebra of braids and ties

TL;DR

This paper constructs faithful tensor representations for the Yokonuma-Hecke algebra and related algebras, providing cellular bases and isomorphisms that advance understanding of their structure and representations.

Contribution

It introduces a faithful tensor representation for the Yokonuma-Hecke algebra and establishes a concrete isomorphism with the modified Ariki-Koike algebra, along with cellular bases for related algebras.

Findings

Faithful tensor representation for Y constructed

Isomorphism between Y and modified Ariki-Koike algebra established

Cellular bases for Y and the algebra of braids and ties provided

Abstract

We construct a faithful tensor representation for the Yokonuma-Hecke algebra Y, and use it to give a concrete isomorphism between Y and Shoji's modified Ariki-Koike algebra. We give a cellular basis for Y and show that the Jucys-Murphy elements for Y are JM-elements in the abstract sense. Finally, we construct a cellular basis for the Aicardi-Juyumaya algebra of braids and ties.