Discrete spectrum of the Weil representation
نویسندگان
چکیده
منابع مشابه
The Weil Representation
This is my senior honors thesis done in my final year as an undergraduate at Stanford University, under the direction of Professor Akshay Venkatesh. We will construct the Weil representation of SL2(R) through a natural action of the Heisenberg group Heis(R) on the space of square-integrable complex-valued functions L 2(R), together with the celebrated Stone-von Neumann theorem of functional ana...
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We survey a new application of the Weil representation to construct a canonical basis Φ of eigenvectors for the discrete Fourier transform (DFT). The transition matrix Θ from the standard basis to Φ defines a novel transform which we call the discrete oscillator transform (DOT for short). In addition, we describe a fast algorithm for computing Θ in certain cases.
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The Segal-Shale-Weil (oscillator) representation
The objects called oscillator representations are decades old, originally developed by physicists for their own purposes. For example, [Weyl 1928], [Stone 1930], [vonNeumann 1931]. Detailed study of the infinitedimensional representation theory of small classical groups appeared first in [Wigner 1939], [Bargmann 1947]. A more modern treatment of oscillator representations began with [Shale 1962...
متن کاملThe Weil Representation in Characteristic Two
In this paper we construct a new variant of the Weil representation, associated with a symplectic vector space (V, ω) defined over a finite field of characteristic two. Our variant is a representation ρ : AMp (V ) → GL (H), where the group AMp (V ) is forth cover of a group ASp (V ), which is a nontrivial gluing of the symplectic group Sp (V ) and the dual group V ∗. In particular, the group AS...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1977
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1977-14299-7