Strongly positive representations of metaplectic groups
نویسندگان
چکیده
منابع مشابه
Principal Series Representations of Metaplectic Groups
We study the principal series representations of central extensions of a split reductive algebraic group by a cyclic group of order n. We compute the Plancherel measure of the representation using Eisenstein series and a comparison method. In addition, we construct genuine central characters of the metaplectic torus in the simply-laced case.
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M. Hanzer and I. Matić have proved that the genuine unitary principal series representations of the metaplectic groups are irreducible. A simple consequence of that paper is a criterion for the irreducibility of the non-unitary principal series representations of the metaplectic groups that we give in this paper.
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where the image of A is in the center of G̃. If G and G̃ are topological groups, and if A is a discrete subgroup of the center of G̃, then we may think of G̃ as a cover of G, in the topological sense. So we will sometimes use the term covering group. Very often for us, A will be the group μn(F ) of n-th roots of unity, in a given field F . We will use this notation only if |μn(F )| = n. By a Metapl...
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In 1952, Gelfand and Fomin noticed that classical modular forms were related to representations of SL2(R). As a result of this realization, Gelfand later defined GLr automorphic forms via representation theory. A metaplectic form is just an automorphic form defined on a cover of GLr, called a metaplectic group. In this talk, we will carefully construct the metaplectic covers of GL2(F) where F i...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2011
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2011.02.015