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The Invariant Part of the Center of the Small Quantum Group

By Oscar Kivinen

Appears in collection : Workshop on Quantum Geometry

The Hitchin fibration has already found many beautiful applications to representation theory, such as Cherednik algebras and automorphic representations. Using the recent work of Bezrukavnikov-Boixeda Alvarez-Shan-Vasserot relating the invariant part of the center of the small quantum group to the geometry of a specific singular Hitchin fiber, we prove a conjecture of Igor Frenkel describing the dimension of the center. Furthermore, when G is of type A, we prove (conditionally on a conjecture of Carlsson-Mellit) that there is a bigraded structure on the center, coinciding with Haiman’s diagonal coinvariant ring. This is joint work with Anna Lachowska and Nicolas Hemelsoet.

Information about the video

  • Date of recording 4/28/22
  • Date of publication 4/28/22
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

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