On a q-Identity Arising from the Dimension of a Representation of GL(n)   over a Finite Field
  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. 
Ofir Gorodetsky and Zahi Hazan
math.RT math.CO