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University of California – Berkeley

1. Beraldo, Dario. Loop group actions on categories and Whittaker invariants.

Degree: Mathematics, 2013, University of California – Berkeley

We develop some aspects of the theory of D-modules on schemes and indschemes of pro-finite type. These notions are used to define D-modules on (algebraic) loop groups and, consequently, actions of loop groups on DG categories. We also extend the Fourier-Deligne transform to Tate vector spaces. Let N be the maximal unipotent subgroup of a reductive group G. For a non-degenerate character c of N((t)), and a category C acted upon by N((t)), there are two possible notions of the category of (N((t)),c)-objects: the invariant category and the coinvariant category. These are the Whittaker categories of C, which are in general not equiva- lent. However, there is always a natural functor T from the coinvariant category to the invariant category. We conjecture that T is an equivalence, provided that the N((t))-action on C is the restriction of a G((t))-action. We prove this conjecture for G=GLn and show that the Whittaker categories can be obtained by taking invariants of C with respect to a very explicit pro-unipotent group subscheme (not indscheme) of G((t)).

Subjects/Keywords: Mathematics; Fourier transform; Heisenberg group; higher categories; Langlands correspondence; loop groups; Whittaker invariants

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Beraldo, D. (2013). Loop group actions on categories and Whittaker invariants. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/0fg9019s

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Beraldo, Dario. “Loop group actions on categories and Whittaker invariants.” 2013. Thesis, University of California – Berkeley. Accessed August 13, 2020. http://www.escholarship.org/uc/item/0fg9019s.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Beraldo, Dario. “Loop group actions on categories and Whittaker invariants.” 2013. Web. 13 Aug 2020.

Vancouver:

Beraldo D. Loop group actions on categories and Whittaker invariants. [Internet] [Thesis]. University of California – Berkeley; 2013. [cited 2020 Aug 13]. Available from: http://www.escholarship.org/uc/item/0fg9019s.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Beraldo D. Loop group actions on categories and Whittaker invariants. [Thesis]. University of California – Berkeley; 2013. Available from: http://www.escholarship.org/uc/item/0fg9019s

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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