Supersingular representations of p-adic reductive groups.

Abstract: The representation theory of p-adic reductive groups plays an extremely important role in modern number theory. Namely, the local Langlands conjectures predict that (packets of) irreducible complex representations of p-adic reductive groups (such as $\mathrm{GL}_n(\mathbb{Q}_p)$, $\mathrm{GSp}_{2n}(\mathbb{Q}_p)$, etc.) should be parametrized by certain representations of the Weil-Deligne group (a variant of the usual absolute Galois group). A special role in this hypothetical correspondence is held by the supercuspidal representations, which generically are expected to correspond to irreducible objects on the Galois side, and which serve as building blocks for all irreducible representations. Motivated by recent advances in the mod-$p$ local Langlands program (i.e., with mod-$p$ coefficients instead of complex coefficients), I will give an overview of what is known about supersingular representations of $p$-adic reductive groups, which are the "mod-$p$ coefficients" analogs of supercuspidal representations. This is joint work with Florian Herzig and Marie-France Vigneras.

number theory

Audience: researchers in the discipline

Comments: Please register for the talks on August 24 here: virginia.zoom.us/meeting/register/tJMkc-uorT8iHdOXRaBkci8wHoKUkqiXaq-E

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POINT: New Developments in Number Theory

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