The character of the metaplectic representation and the character formula for certain representations of an almost algebraic Lie group over a \(p\)-adic field (Q1295921)

It is known that the character of the Weil representation of a metaplectic group over a local field \(k\) is a locally integrable function, which is smooth on the set of regular semi-simple elements. It has been computed in the case \(k = {\mathbb R}\). In the present article \(k\) is \(p\)-adic of characteristic zero. An explicit formula is given for the character of the metaplectic representation as a locally constant function on an open set which is larger than the set of regular semi-simple elements. The method consists mainly of Harish-Chandra's descent and the explicit calculation of the character of representations of the Heisenberg group. In the second half of the paper the former results are used to prove a character formula in the neighbourhood of a semi-simple element for certain irreducible unitary representations of almost algebraic \(p\)-adic groups.