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Algebra & Combinatorics Seminar

Title: 2-Categorification of Category O and 3d Mirror Symmetry
Speaker: Justin Hilburn (Perimeter Institute, Waterloo, Canada)
Date: 17 February 2023
Time: 3 pm
Venue: LH-1, Mathematics Department

In 1976 Bernstein, Gelfand, and Gelfand introduced Category $\mathcal{O}$ for a semi-simple Lie algebra $\mathfrak{g}$. This is roughly the smallest sub-category of $\mathfrak{g}$-mod containing the Verma modules and such that the simple modules have projective covers. After work of Beilinson–Bernstein and Beilinson–Ginzburg–Soergel it became clear that the the good homological properties of this category were due to the fact that it can be identified with a category of perverse sheaves on the flag variety $G/B$.

In this talk I will show how this story fits into the physics of 3d mirror symmetry. This leads to conjectural 2-categorifications of category $\mathcal{O}$ that can be computed explicitly for $\mathfrak{g} = \mathfrak{sl}_2$.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 24 Mar 2023