PIRSA:17110064 Scientific Series Mathematical physics

DOI10.48660/17110064

Series: Mathematical Physics

Makisumi, S. (2017). Modular Koszul duality for Kac–Moody groups. Perimeter Institute. https://pirsa.org/17110064

Makisumi, Shotaro. Modular Koszul duality for Kac–Moody groups. Perimeter Institute, Nov. 27, 2017, https://pirsa.org/17110064 

@misc{ pirsa_PIRSA:17110064,
  doi = {10.48660/17110064},
  url = {https://pirsa.org/17110064},
  author = {Makisumi, Shotaro},
  keywords = {Mathematical physics},
  language = {en},
  title = {Modular Koszul duality for Kac{\textendash}Moody groups},
  publisher = {Perimeter Institute},
  year = {2017},
  month = {nov},
  note = {PIRSA:17110064 see, \url{https://pirsa.org}}
}

Abstract

The Hecke category is a certain monoidal category of constructible sheaves on a flag variety that categorifies the Hecke algebra and plays an important role in geometric representation theory. In this talk, I will discuss a monoidal Koszul duality relating the Hecke category of Langlands-dual (Kac–Moody) flag varieties, categorifying a certain involution of the Hecke algebra. In particular, I will try to explain why one needs to introduce a monoidal category of "free-monodromic tilting sheaves" to formulate this duality. (Joint with P.N. Achar, S. Riche, and G. Williamson.)

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