Colloquium abstracts

Sandeep Varma
TIFR
November 28, 2013

On a Result of Moeglin and Waldspurger in Residual Characteristic 2':  Let $F$ be a finite extension of $\QQ_p$, ${\bf G}$ a connected reductive group over $F$, and $\pi$ an irreducible admissible representation of ${\bf G}(F)$. A result of C. Moeglin and J.-L. Waldspurger states that, if the residual characteristic of $F$ is different from $2$, then the `leading' coefficients in the character expansion of $\pi$ at the identity element of ${\bf G}(F)$ give the dimensions of certain spaces of degenerate Whittaker forms. We discuss how to extend their result to residual characteristic $2$. The outline of the proof is the same as in the original paper of Moeglin and Waldspurger, but certain constructions need to be modified to accommodate the case of even residual characteristic.