Published on *Department of Mathematics* (https://math.yale.edu)

November 16, 2021 - 4:30pm

Zoom

The supercuspidal representation is a building block for constructing representations of a general linear group over $p$-adic fields.

This representation is further classified by the type theory due to Bushnell-Kutzko. It turns out that this structural information of the representation theory is encoded in local Rankin-Selberg factors for pairs.

Keeping the spirit, Paskunas and Stevens establish an expression of local factors in terms of those of the depth zero data. The purpose of this talk is to carry over their approach for computing the Langlands-Shahidi local coefficient for pairs through the theory of types and covers. In the process, we recover a well-known equality of local factors and the Plancherel formula by Shahidi. This is joint work with Muthu Krishnamurthy.