Kirillov-Duflo orbit method and minimal representations of simple groups over a local field of characteristic zero

DOI10.1215/S0012-7094-97-09009-8zbMath0941.22017OpenAlexW1574670700MaRDI QIDQ1376030

Pierre Torasso

Publication date: 1 August 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-97-09009-8

zbMATH Keywords

irreducible unitary representationsmetaplectic representationminimal representationorbit methodinduced representationnilpotent coadjoint orbit

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Representations of Lie and linear algebraic groups over local fields (22E50) Induced representations for locally compact groups (22D30) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items

Admissible nilpotent coadjoint orbits of p-adic reductive Lie groups, On the wavefront sets associated with theta representations, Unnamed Item, Theta distinguished representations, inflation and the symmetric square \(L\)-function, Unnamed Item, Classification of minimal representations of real simple Lie groups, Integral formula of the unitary inversion operator for the minimal representation of \(\text{O}(p,q)\), A notion of rank for unitary representations of reductive groups based on Kirillov's orbit method, A superunitary Fock model of the exceptional Lie supergroup \(\mathbb{D}(2, 1; \alpha)\), Analysis on the minimal representation of \(O(p,q)\). I: Realization via conformal geometry., Global uniqueness of small representations, On minimal representations of Chevalley groups of type \(D_n\), \(E_n\) and \(G_{2}\), Minimal representations via Bessel operators, THE DOUBLE COVER OF ODD GENERAL SPIN GROUPS, SMALL REPRESENTATIONS, AND APPLICATIONS, Isolatedness of the minimal representation and minimal decay of exceptional groups, Integral formulas for the minimal representation of \(O(p,2\)), Small principal series and exceptional duality for two simply laced exceptional groups, The Schrödinger model for the minimal representation of the indefinite orthogonal group 𝑂(𝑝,𝑞), Geometrizing the minimal representations of even orthogonal groups, Covariant quantization: spectral analysis versus deformation theory, Geometric quantization of real minimal nilpotent orbits, Rank and matrix coefficients for simply laced groups, Non-local equivariant star product on the minimal nilpotent orbit

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