Local Constants for Heisenberg Representations

Abstract

We can attach a local constant to every finite dimensional continuous complex representation of a local Galois group of a non-archimedean local field $F/{\mathbb{Q}}_p$ by Deligne and Langlands. Tate \cite{JT1} gives an explicit formula for computing local constants for linear characters of $F^{\times }$, but there is no explicit formula of local constant for any arbitrary representation of a local Galois group. In this article we study Heisenberg representations of the absolute Galois group $G_F$ of $F$ and give invariant formulas of local constants for Heisenberg representations of dimension prime to $p$.

arXiv commentp. 46. The object of this paper is the same as the first draft. Expect a few parts (in section 2), this paper is different from the first draft

Cited by in corpus (1)

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