Geometry of local Arthur packets for simple unramified Arthur parameters for GLn

Seminar: 
Algebra and Number Theory Seminar
Event time: 
Tuesday, November 2, 2021 - 4:30pm
Location: 
Zoom
Speaker: 
Mishty Ray
Speaker affiliation: 
University of Calgary
Event description: 

The local Langlands correspondence for a connected reductive p-adic group G partitions the set of equivalence classes of smooth irreducible representations of G(F) into L-packets using equivalence classes of Langlands parameters. Vogan's geometric perspective gives us a moduli space of Langlands parameters, and the correspondence can be viewed as a relation between the set of equivalence classes of smooth irreducible representations of G(F) and simple objects in the category of equivariant perverse sheaves on the moduli space of Langlands parameters that share a common infinitesimal parameter. This geometry gives us the notion of an ABV-packet, a set of smooth irreducible representations of G(F), which conjecturally generalizes the notion of a local Arthur packet - a local Arthur packet is conjecturally an ABV-packet. In this talk, we will look at Langlands parameters coming from simple Arthur parameters in the case of GLn. We will explore the geometry of the moduli space of Langlands parameters using an example. We will see work in progress towards proving that the local Arthur packet is the ABV-packet for this case.

Research Area(s):