Some Genuine Small Representations of a Nonlinear Double Cover

DOI10.1090/TRAN/7351zbMath1516.22009arXiv1412.4274WikidataQ129332241 ScholiaQ129332241MaRDI QIDQ6257248

Publication date: 13 December 2014

Abstract: Let G be the real points of a simply connected, semisimple, simply laced complex Lie group, and let ilde{G} be the nonlinear double cover of G. We discuss a set of small genuine irreducible representations of ilde{G} which can be characterized by the following properties: (a) the infinitesimal character is ho/2; (b) they have maximal tau-invariant; (c) they have a particular associated variety O. When G is split, we construct them explicitly. Furthermore, in many cases, there is a one-to-one correspondence between these small representations and the pairs (genuine central characters of ilde{G}, real forms of O) via the map pi mapped to (central character of pi, real associated variety of pi).

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Semisimple Lie groups and their representations (22E46) General properties and structure of complex Lie groups (22E10) General properties and structure of real Lie groups (22E15) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

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