Yokonuma-Hecke algebra

introduction

def (Yokonuma--Hecke algebra)

The Yokonuma--Hecke algebra $Y_{d,n}$ is generated by elements $$g_1,\ldots,g_{n-1},t_1,\ldots,t_n,$$ subject to the following defining relations : $$ \label{def-1} \begin{array}{rclcl} g_ig_j & = & g_jg_i &\ & \mbox{for $i,j=1,\ldots,n-1$ such that $\vert i-j\vert > 1$,}\\ g_ig_{i+1}g_i & = & g_{i+1}g_ig_{i+1} && \mbox{for $i=1,\ldots,n-2$,} \end{array} $$