2025 CMS Summer Meeting
Quebec City, June 6 - 9, 2025
Groups over local fields and their representations
Org: Paul Mezo (Carleton University) and Monica Nevins (University of Ottawa)
Org: Paul Mezo (Carleton University) and Monica Nevins (University of Ottawa)
- NICOLAS ARANCIBIA-ROBERT, Université de Paris, Cergy
- SERINE BAIRAKJI, Ottawa
- KRISTAPS BALODIS, University of Calgary
Representation-theoretic consequences of the geometry of Vogan varieties. [PDF]
- SERINE BAIRAKJI, Ottawa
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Building on the work of Zelevisnky and the cases for real and complex groups, Davis Vogan purposed a $p$-adic Kazhdan-Lusztig hypothesis ($p$-KLH): The dimensions of stalks of perverse sheaves on varieties $V_\lambda$ of Langlands parameters having fixed infinitesimal parameter $\lambda$, should coincide with multiplicities of irreducible representations of infinitesimal parameter $\lambda$ in standard representations.
Moreover, Vogan defined what we call ABV-packets in terms of the microlocal geometry of $V_\lambda$, and purposed that these coincide with Arthur's A-packets.
We will discuss recent work which, under the assumption of the $p$-KLH, proves a conjecture of Gross-Prasad that an L-packet $\Pi_\phi(G)$ contains a generic representation if and only if $L(s, \phi, \mathrm{Ad})$ is regular at $s=1$. We also discuss implications for Shahidi's enhanced genericity conjecture, and an analogue for ABV-packets. Time permitting, we may also offer some speculation as to the relationship between Arthur parameters and orbits of smooth closure.
- ADÈLE BOURGEOIS, Tutte Institute
- MATHILDE GERBELLI-GAUTHIER, Toronto
- JULIA GORDON, UBC
- ALEX HAZELTINE, Michigan
- ZANDER KARAGANIS, Toronto
- GIL MOSS, Maine
- ISABELLA NEGRINI, Toronto
- MISHTY RAY, Carleton
- HADI SALMASIAN, Ottawa
- LOREN SPICE, TCU, USA
- EKTA TIWARI, Ottawa
- TIAN AN WONG, Michigan
- MATHILDE GERBELLI-GAUTHIER, Toronto