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

Locations: Zoom, Calgary, Paris, Lethbridge

Andrew, Bin and Clifton
Zoom, Lethbridge, Beijing and Calgary

Speaker: Andrew Fiori

Location: Zoom, Paris, Calgary and Lethbridge

Topic: Progress on the Fourier transform and induction for Vogan varieties!
Details in our github repo.

Speaker: Andrew Fiori

Location: Zoom, Beijing, Calgary and Lethbridge

Topic: How to enumerate all stata in Vogan varieties for GL(n). Quivers perspective.
Some observations about the Kashiwara-Saito singularity in the Vogan variety for GL(16).

Speaker: Reginald Lybbert

Location: Calgary, MS337

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

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