Arithmetic invariants of discrete Langlands parameters

Arithmetic invariants of discrete Langlands parameters

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B. Gross, Harvard University
IAS - Simonyi Hall Seminar Room SH-101

Let $G$ be a reductive algebraic group over a local field $k$. Hiraga, Ichino and Ikeda have recently proposed a general conjecture for the formal degree of a discrete series representation of $G(k)$, using special values of the adjoint L-function and $\epsilon$ factor of its (conjectural) Langlands parameter. I will reformulate this conjecture using Euler-Poincare measure on $G(k)$ and the motive of $G$, establish a key rationality property of the ratio of special values in the non-Archimedean case, and explore some of its implications for supercuspidal parameters.This is joint work with Mark Reeder.