This article is cited in 2 papers

Harmonic Analysis on a Class of Spherical Homogeneous Spaces

N. E. Gorfinkel

M. V. Lomonosov Moscow State University

Abstract: The spectrum of representations of a semisimple algebraic group in spaces of sections of homogeneous linear bundles on a certain class of spherical homogeneous spaces is studied; the algebra of invariant functions on the cotangent bundles of spaces from this class and invariant differential operators are described.

Keywords: semisimple complex algebraic group, irreducible representation, homogenous space, homogeneous linear bundle, spherical homogeneous space, cotangent bundle, invariant differential operator, Borel subgroup, universal enveloping algebra.

UDC: 512.745+512.816.4

Received: 27.05.2010
Revised: 01.12.2010

DOI: 10.4213/mzm8826

 English version: Mathematical Notes, 2011, 90:5, 678–685

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