Maximal hypoellipticity and Dolbeault cohomology representations for U(p,q)

Details Maximal hypoellipticity and Dolbeault cohomology representations for U(p,q) Maximal hypoellipticity and Dolbeault cohomology representations for U(p,q)

2007-05-19

arxiv.org/abs/0705.2800v1

Mathematics

Representation Theory

14 pages, preprint, LaTeX

Scientific paper

Let Y=G/L be a flag manifold for a reductive G and K a maximal compact subgroup of G. We define an equivariant differential operator on G/(L cap K) playing the role of an equivariant Dolbeault Laplacian when restricted to the complex manifold G/L, using a distribution transverse to the fibers and satisfying the Hormander condition. We prove here that this operator is not maximal hypoelliptic when G=U(p,q).

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