An upper bound on conductors for pairs. (English) Zbl 0884.11049
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.
Reviewer: Yuval Z.Flicker (Columbus/Ohio)
MSC:
| 11S37 | Langlands-Weil conjectures, nonabelian class field theory |
| 20G25 | Linear algebraic groups over local fields and their integers |
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