Hecke algebras for $p$-adic groups and the explicit local Langlands correspondence for $\mathrm{G}_2$

Abstract: I will talk about my recent joint work with Aubert where we prove the local Langlands conjecture for $\mathrm{G}_2$ (explicitly). This uses our earlier results on Hecke algebras attached to Bernstein components of reductive $p$-adic groups, as well as an expected property on cuspidal support, along with a list of characterizing properties. In particular, we obtain "mixed" $L$-packets containing $F$-singular supercuspidals and non-supercuspidals.

number theory

Audience: researchers in the topic

Harvard number theory seminar