Geometric quantization and derived functor modules for semisimple Lie groups

  title={Geometric quantization and derived functor modules for semisimple Lie groups},
  author={Wilfried Schmid and Joseph A. Wolf},
  journal={Journal of Functional Analysis},
  • W. Schmid, J. Wolf
  • Published 1 April 1990
  • Mathematics
  • Journal of Functional Analysis
Two geometric character formulas for reductive Lie groups
In this paper we prove two formulas for the characters of representations of reductive groups. Both express the character of a representation π in terms of the same geometric data attached to π. When
Finite Rank Homogeneous Holomorphic Bundles in Flag Spaces
For more than forty years the study of homogeneous holomorphic vector bundles has resulted in an important source of irreducible unitary representations for a real reductive Lie group. In the mid
Weyl Group Actions on Lagrangian Cycles and Rossmann’s Formula
Let G R be a connected Lie group, g R its Lie algebra, and g R * the vector space dual of g R . Each coadjoint orbit, i.e., G R -orbit in g R *, has an intrinsically defined G R -invariant symplectic
An interesting class of irreducible unitary representations of semisimple Lie groups consists of the representations associated to elliptic coadjoint orbits. An important open problem is to give a
Quasi-Equivariant D -Modules, Equivariant Derived Category, and Representations of Reductive Lie Groups
In this note, we describe proofs of certain conjectures on functorial, geometric constructions of representations of a reductive Lie group G R . Our methods have applications beyond the conjectures
Complex Geometry and Representations of Lie Groups
Let Z = G/Q be a complex flag manifold and let Go be a real form of G. Then the representation theory of the real reductive Lie group Go is intimately connected with the geometry of Go-orbits on Z.
Compact Subvarieties in Flag Domains
A real reductive Lie group G 0 acts on complex flag manifolds G/Q, where Q is a parabolic subgroup of the complexification G of G 0. The open orbits D = G 0(x) include the homogeneous complex
On quaternionic discrete series representations, and their continuations.
Among the discrete series representations of a real reductive group G, the simplest family to study are the holomorphic discrete series. These representations exist when the Symmetrie space G/ K has
Let D be a noncompact complex manifold which fits into a holomorphic double fibration D ← W → M. We describe the construction of a transform from the Dolbeault cohomology space H s (D,O(E)) into a


Localization and standard modules for real semisimple Lie groups I: The duality theorem
In this paper we relate two constructions of representations of semisimple Lie groups constructions that appear quite different at first glance. Homogeneous vector bundles are one source of
Homogeneous complex manifolds and representations of semisimple lie groups.
  • W. Schmid
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1968
The generalized Borel-Weil theorem and Theorem 1 are proved, which show that the structure of a holomorphic line bundle such that the action of G on D lifts to the sheaf of germs of holomorphic sections of Lx, O(L,) is an infinite-dimensional Frechet space on which G acts continuously.
Some properties of square-integrable representations of semisimple Lie groups
In the theory of irreducible representations of a compact Lie group, the formula for the multiplicity of a weight and the so-called theorem of the highest weight are among the most important results.
A proof of Blattner's conjecture
Let G be a connected, semisimple Lie group. In Harish-Chandra's work on the Plancherel formula, the discrete series of irreducible unitary representations [5] plays a crucial role. Roughly speaking,
1. The trace formula of Selberg reduces the problem of calculating the dimension of a space of automorphic forms, at least when there is a compact fundamental domain, to the evaluation of certain
A Generalization of Casselman’s Submodule Theorem
Let Gℝ be a real reductive Lie group, g;ℝ its Lie algebra. Let M be an irreducible Harish-Chandra module. Using some fine analytic arguments, based on the study of asymptotic behavior of matrix
The Plancherel theorem for general semisimple groups
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