Events

Calculation of the characteristic cycles of the Kashiwara-Saito singularity

Speaker: Reggie Lybbert

In their 1997 paper, _Geometric construction of crystal bases_ (Duke Math Journal, Vol 89, No. 1), Masaki Kashiwara and Yoshihisa Kashiwa Saito described a singularity in a quiver representation variety of type A_5 with the property that the characteristic cycles of the singularity is reducible, this providing a counterexample to a conjecture of Kazhdan and Lusztig. This singularity is now commonly know at the Kashiwara-Saito singularity. While the 1997 paper showed that the characteristic cycles of the Kashiwara-Saito singularity decomposes into at least two irreducible cycles, they promised, but did not prove, that it decomposes into exactly two irreducible cycles. Using techniques developed in the example part of the Voganish paper, augmented by some computational tools developed this summer, we believe we have a proof of this promise. In this seminar we'll give a sketch of the proof.

Using this calculation and the local Langlands correspondence for GL(16), we should be able to exhibit an irreducible representation \pi of p-adic GL(16) with the property that its ABV-packet (as defined in the Voganish paper) contains exactly one other irreducible representation, \pi', and also describe that representation. We refer to this \pi as the Kashiwara-Saito representation of GL(16) and to \pi' as its coronal representation. This will provide the smallest known example of an irreducible representation of p-adic general linear group with one coronal representation.

Locations: Zoom (https://zoom.us/j/238450154), Calgary, Lethbridge

Event Date: 
Tuesday, July 24, 2018 -
10:00 to 11:30
Event Type: 
Project: 
Voganish Project

Summer Student Research Seminar on the Kashiwara-Saito singularity

Overview of the Voganish Project

Statement of summer objectives: Microlocal vanishing cycles of the Kashiwara-Saito singularity

Divide and conquer:
Nicole Kitt: Calculations using the Fourier transform
Reginald Lybbert: Calculations using resolution of singularities

Location: University of Calgary, MS 337

Event Date: 
Tuesday, May 1, 2018 -
10:00 to 11:30
Event Type: 
Project: 
Voganish Project

Fourier transform of equivariant perverse sheaves

The Fourier transform we're using is taken from Kashiwara and Shapira by way of Schurmann, and has the vanishing cycles functor built in. Today we're working on establishing and documenting the main properties of this functor.

Andrew and Clifton, at the University of Lethbridge

Event Date: 
Saturday, April 14, 2018 -
10:00 to 16:00
Event Type: 
Project: 
Voganish Seminar

Construction of supercuspidal representations

Speaker: Kam-Fai Tam (Max-Planck-Institut für Mathematik, Bonn)

Title: Construction of supercuspidal representations

Location: Hilbert Seminar Room (MS 337)

Time: Thursday, April 5, 14:00--15:00

Abstract: Given a supercuspidal representation of GL_2 over a p-adic field or the group U_2 of 2-by-2 unitary matrices relative to a quadratic p-adic field extension, we explain how to use the internal structure of its Langlands parameter to construct a underlying type of this representation. (If time permits, we will also cover a construction of discrete series representations.)

Event Date: 
Thursday, April 5, 2018 -
14:00 to 15:00
Event Type: 

Pages