On a q-Identity Arising from the Dimension of a Representation of GL(n) over a Finite Field

Abstract

The present paper proves a $q$-identity, which arises from a representation ${\pi }_{N,\psi }$ of ${\text{GL}}_n({\mathbb{F}}_q)$. This identity gives a significant simplification for the dimension of ${\pi }_{N,\psi }$, which allowed the second author to obtain a description of the representation.

12 pages. Comments are welcome