Maximal hypoellipticity and dolbeault cohomology representations for u(p,q) (2008).

Content Provider	CiteSeerX
Author	Prudhon, Nicolas Strasbourg, Irma
Abstract	Let Y = G/L be a flag manifold for a reductive G and K a maximal compact subgroup of G. We define here an equivariant differential operator on G/L∩K playing the role of an equivariant Dolbeault Laplacian for the complex manifold G/L, using a distribution transverse to the fibers of G/L∩K → G/L and satisfying the Hörmander condition. We prove here that this operator is not maximal hypoelliptic. Introdution There are two challenging problems in representation theory of Lie groups. The first one is to classify unitary representations for large classes of Lie groups. Connected nilpotent Lie groups form such a class, and Kirillov established, for any connected nilpotent Lie group, a bijective correspondance between the set of coadjoint orbits and the set of (equivalence classes of) unitary irreducible representations of the group. This approach lead to the second problem: to realize unitary representations geometrically. These two problems are still open for reductive groups, but the technique of coadjoint orbits is a constant source of inspiration. For reductive groups there
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Publisher Date	2008-01-01
Access Restriction	Open
Subject Keyword	Maximal Hypoellipticity Dolbeault Cohomology Representation Lie Group Unitary Representation Reductive Group Coadjoint Orbit Equivalence Class Maximal Compact Subgroup Nilpotent Lie Group Large Class Flag Manifold Equivariant Differential Operator Unitary Irreducible Representation Distribution Transverse Representation Theory Second Problem Complex Manifold First One Rmander Condition Approach Lead Constant Source Connected Nilpotent Lie Group Bijective Correspondance Equivariant Dolbeault Laplacian
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