Orateur
Description
Let $G$ be a real reductive group with Lie algebra $\mathfrak{g}$ and let $K \subset G$ be a maximal compact subgroup.
The heart of the algebraic representation theory of $G$ consists in the study of $(\mathfrak{g},K)$-modules. The latter correspond to modules over a certain approximately unital ring $R$, known as the Hecke algebra of the pair $(\mathfrak{g},K)$. The contraction of $G$ onto its motion group $G_0$ naturally defines an algebraic family of rings $(R_t)_t$ over the affine line, with $R_t = R$ if $t\neq 0$ and $R_0$ being the Hecke algebra of the pair $(\mathfrak{g}_0,K)$ defined by the Cartan motion group. In this talk, we present a recent result showing that this algebraic family of rings is, in a sense, piecewise constant. We will then explain consequences for the continuity of the Mackey bijection.