Vogan Duality for Nonlinear Type B
نویسنده
چکیده
Let G = Spin[4n+1] be the connected, simply connected complex Lie group of type B2n and let G = Spin(p, q) (p + q = 4n + 1) denote a (connected) real form. If q / ∈ {0, 1}, G has a nontrivial fundamental group and we denote the corresponding nonalgebraic double cover by G̃ = ̃ Spin(p, q). The main purpose of this paper is to describe a symmetry in the set of genuine parameters for the various G̃ at certain half-integral infinitesimal characters. This symmetry is used to establish a duality of the corresponding generalized Hecke modules and ultimately results in a character multiplicity duality for the genuine characters of G̃.
منابع مشابه
Irreducible Genuine Characters of the Metaplectic Group: Kazhdan-lusztig Algorithm and Vogan Duality
We establish a Kazhdan-Lusztig algorithm to compute characters of irreducible genuine representations of the (nonlinear) metaplectic group with half-integral infinitesimal character. We then prove a character multiplicity duality theorem for representations of Mp(2n,R) at fixed half-integral infinitesimal character. This allows us to extend some of Langlands’ ideas to Mp(2n,R).
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