# Kazhdan-Lusztig correspondence for a class of Lie superalgebras

### APA

Niu, W. (2023). Kazhdan-Lusztig correspondence for a class of Lie superalgebras. Perimeter Institute. https://pirsa.org/23100111

### MLA

Niu, Wenjun. Kazhdan-Lusztig correspondence for a class of Lie superalgebras. Perimeter Institute, Oct. 26, 2023, https://pirsa.org/23100111

### BibTex

@misc{ pirsa_PIRSA:23100111, doi = {10.48660/23100111}, url = {https://pirsa.org/23100111}, author = {Niu, Wenjun}, keywords = {Mathematical physics}, language = {en}, title = {Kazhdan-Lusztig correspondence for a class of Lie superalgebras}, publisher = {Perimeter Institute}, year = {2023}, month = {oct}, note = {PIRSA:23100111 see, \url{https://pirsa.org}} }

Wenjun Niu Perimeter Institute for Theoretical Physics

## Abstract

For a simple Lie algebra \mathfrak{g}, Kazhdan-Lusztig correspondence states that for certain values of the level k, there is an equivalence between two braided tensor categories: the category of modules of the affine Lie algebra of \mathfrak{g} at level k and the category of modules of the quantum group of \mathfrak{g} at q=e^{\pi i/k}. I will report on recent work to appear with T. Creutzig and T. Dimofte proving such a statement for a class of Lie superalgebras. These Lie superalgebras and their affine VOAs arise from the study of boundary conditions in 3d \mathcal{N}=4 abelian gauge theories. I will also explain how the corresponding supergroups act on the category of matrix factorizations.

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