#### Algebra & Combinatorics Seminar

##### Venue: Microsoft Teams (online)

Let $G$ be the group $SL_2$ over a finite extension $F$ of $\mathbb{Q}_p$, $p$ odd. I will discuss certain distributions on $G(F)$, belonging to what is called its Bernstein center (I will explain what this and many other terms in this abstract mean), supported in a certain explicit subset of $G(F)$ arising from the work of A. Moy and G. Prasad. The assertion is that these distributions form a subring of the Bernstein center, and that convolution with these distributions has very agreeable properties with respect to orbital integrals. These are ‘depth $r$ versions’ of results proved for general reductive groups by J.-F. Dat, R. Bezrukavnikov, A. Braverman and D. Kazhdan.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 01 Oct 2020