An explicit conductor formula for $\operatorname{GL} _{n} \times \operatorname{GL} _{1}$

Abstract

We prove an explicit formula for the conductor of an irreducible, admissible representation of $\operatorname{GL} _{n}(F)$ twisted by a character of $F^{\times} $ where the field $F$ is local and non-archimedean. As a consequence, we quantify the number of character twists of such a representation of fixed conductor.