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Alexander Braverman

  1. Representations of affine Kac-Moody groups over local and global fields: a survey of some recent results.

    Mon, 05/07/2012 - 15:01 — SomNambul
    Authors: Alexander Braverman, David Kazhdan
    Subjects: Representation Theory
    Abstract

    Let G be a reductive algebraic group over a local field K or a global field
    F. It is well know that there exists a non-trivial and interesting
    representation theory of the group G(K) as well as the theory of automorphic
    forms on the corresponding adelic group. The purpose of this paper is to give a
    survey of some recent constructions and results, which show that there should
    exist an analog of the above theories in the case when G is replaced by the
    corresponding affine Kac-Moody group (which is essentially built from the
    formal loop group G((t)) of G).

  2. Affine Gindikin-Karpelevich formula via Uhlenbeck spaces.

    Thu, 12/31/2009 - 16:01 — SomNambul
    Authors: Alexander Braverman, Michael Finkelberg, David Kazhdan
    Subjects: Representation Theory
    Abstract

    We prove a version of the Gindikin-Karpelevich formula for untwisted affine
    Kac-Moody groups over a local field of positive characteristic.

  3. Pursuing the double affine Grassmannian II: Convolution.

    Tue, 08/25/2009 - 22:41 — SomNambul
    Authors: Alexander Braverman, Michael Finkelberg
    Subjects: Algebraic Geometry
    Abstract

    This is the second paper of a series (started by arXiv:0711.2083) which
    describes a conjectural analog of the affine Grassmannian for affine Kac-Moody
    groups (also known as the double affine Grassmannian). The current paper is
    dedicated to describing a conjectural analog of the convolution diagram for the
    double affine Grassmannian. In the case when G=SL(n) our conjectures can be
    derived from arXiv:0809.2605.

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