An upper bound on conductors for pairs
Let \(a\), \(b\), \(c\) be the exponents (defined by means of the \(\varepsilon\) factors) of the irreducible admissible representations \(\pi\), \(\rho\), \(\pi\times\rho\) of \(GL(m,F)\), \(GL(n,F)\), \(GL(m,F)\times GL(n,F)\). Here \(F\) is a \(p\)-adic field. It is shown that \(c\leq na+mb-\min(a,b)\) using the essential vector in the Whittaker model in the generic case.
conductors of representations of \(GL(n)\) over a \(p\)-adic field
scientific article; zbMATH DE number 1048747
scientific article