Character formula for representations of local quaternion algebras (wildly ramified case)
Let \(F\) be a non-archimedean local field of characteristic zero and \(D\) the quaternion field over \(F\). In the paper by \textit{H. Hijikata, H. Saito} and \textit{M. Yamauchi} [J. Number Theory 43, 123-167 (1993; Zbl 0819.11018)], the character of an irreducible admissible representation of \(D^{\times}\) was computed explicitly in the case of residual characteristic \(\neq 2\). In the present paper the author applies the same technique to compute that character in the case of residual characteristic \(2\). The character formula has been written out completely only for \(F\) unramified over \(\mathbb{Q}_2\), where it covers already three pages.
scientific article; zbMATH DE number 950586