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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 asignificant simplification for the dimension of $\pi_{N,\psi}$, which allowedthe second author to obtain a description of the representation.

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