Abstract: Not much is known on the ℓ-modular or ℓ-integral representation theory of p-adic groups, beyond the case of GLn. Even worse, the main property used by Vigneras in her treatment of the GLn case is now known to generally fail for other groups. Inspired by the theory of Jordan decomposition” for ℓ-blocks of finite reductive groups, we have conjectured the existence of a decomposition of ℓ-integral representations into factors parametrized by Langlands parameters with source the prime-to-ℓ inertia subgroup, and which obeys some version of the Langlands functoriality principle associated to a morphism of L-groups. I will discuss recent progress on this conjectural picture, both for depth 0 and for positive depth representations.
As usual, the seminar will be preceded by various study groups, starting at 1200.
The talks will be preceded by tea/coffee in Imperial’s common room (room 549 Huxley) from 3:30.