SMS scnews item created by Tom Goertzen at Mon 16 Mar 2026 0822
Type: Seminar
Distribution: World
Expiry: 22 Mar 2026
Calendar1: 20 Mar 2026 1200-1300
CalLoc1: Carslaw 175
CalTitle1: Complex Rank Parabolic Category O via Tensor Product Categorifications
Auth: goertzen@1.145.103.12 (tgoe0324) in SMS-SAML
Algebra Seminar
Complex Rank Parabolic Category O via Tensor Product Categorifications
Wan
Hamilton Wan (MIT) will be speaking in the algebra seminar. We will go out for lunch
after the talk---all are welcome to join!
When: 12-1pm Friday March 20
Where: Carslaw 175
Title: Complex Rank Parabolic Category \(\mathcal{O}\) via Tensor Product
Categorifications
Abstract: Deligne’s categories are symmetric tensor categories that provide a
setting for interpolating classical representation-theoretic constructions beyond
integer rank. In this talk, I will discuss a complex rank variant of the BGG category O
inside Deligne’s categories and explain how, under suitable assumptions, the
characters of simple objects can be described in terms of stable limits of parabolic
Kazhdan—Lusztig polynomials. In fact, these character formulas are shadows of a
deeper structural result: along certain locally closed strata in parameter space, the
complex rank categories O are all equivalent to each other, and actually equivalent to a
stable limit of classical parabolic categories O. The guiding philosophy is the
rigidity of highest weight categories equipped with a compatible categorical action of
the Lie algebra \(\mathfrak{sl}_\infty\). I will explain how the complex rank
categories O fit into this categorification framework, and time permitting, I will
sketch the corresponding uniqueness result for categorifications of tensor products of
highest and lowest weight Fock spaces.
Actions:
Calendar
(ICS file) download, for import into your favourite calendar application
UNCLUTTER
for printing
AUTHENTICATE to mark the scnews item as read