Sep 01. 2025, 15:30 — 16:30
Automorphic minimal representations for simply laced groups are realized
as residues of degenerate Eisenstein series. In the talk we consider their local
compoments.
Let $G$ be a simply-laced group with a maximal parabolic subgroup $P=MN$ such
that N is abelian. The minimal representation $\Pi$ of $G$ admits a model
on $L^2(X_Q)$, where $X_Q=[Q,Q]\backslash M$ a basic affine space of $M$,
with geometric action of $P$. We describe an action of an additional
element s conjugating $P$ to the opposite parabolic $\bar P$
and relate it to the Braverman-Kazhdan operator $L^2(X_Q)\rightarrow L^2(X_{\bar Q})$.
We will discuss the cases $G=E_7$ and $E_6$. This is joint work with Wee Teck Gan.