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Twisted Heisenberg Central Extensions and the Affine ADE Basic Representation


Zhang, Victor (2022) Twisted Heisenberg Central Extensions and the Affine ADE Basic Representation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/42v3-ws41.


We study various aspects of the representation theory of loop groups, all with the aim of giving geometric constructions, parameterized by conjugacy classes of the Weyl group, of the basic representation of the affine Lie algebras associated to a simply laced simple Lie algebra as a restriction isomorphism on dual sections of the level 1 line bundle on the affine Grassmannian. Along the way, we obtain various results on the structure of loop tori, the definition of a notion of a Heisenberg Central extension as an alternative for twisted modules over the lattice vertex algebra and the determination of their representation theory, some computations on central extensions of a torus over a field by K2, and a new proof of the classification of the conjugacy classes of the Weyl group by parabolic induction.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Algebraic geometry, geometric representation theory, loop groups, affine Lie algebra.
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Apostol Award for Excellence in Teaching in Mathematics, 2020.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Zhu, Xinwen
Thesis Committee:
  • Graber, Thomas B. (chair)
  • Flach, Matthias
  • Rains, Eric M.
  • Zhu, Xinwen
Defense Date:25 May 2022
Record Number:CaltechTHESIS:05272022-215641742
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14644
Deposited By: Victor Zhang
Deposited On:31 May 2022 23:16
Last Modified:03 Aug 2022 21:13

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