PIRSA:23100111

Kazhdan-Lusztig correspondence for a class of Lie superalgebras

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

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

          @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

Talk numberPIRSA:23100111
DOI10.48660/23100111
Collection
Talk Type Scientific Series
Subject

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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