Unitary Representations and Complex Analysis

@inproceedings{Vogan2008UnitaryRA,
  title={Unitary Representations and Complex Analysis},
  author={David A. Vogan},
  year={2008}
}
One of the great classical theorems of representation theory is the Borel-Weil Theorem, which realizes any irreducible unitary representation of a compact connected Lie group as the space of holomorphic sections of a complex line bundle on a homogeneous space. These lectures concern two closely related questions: 1. Why should something like the Borel-Weil Theorem be true? 2. Can it usefully be extended to other Lie groups? 
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21 Citations
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3
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Methods Citations
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21 Citations

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Analytic torsion, dynamical zeta functions, and the Fried conjecture
We prove the equality of the analytic torsion and the value at zero of a Ruelle dynamical zeta function associated with an acyclic unitarily flat vector bundle on a closed locally symmetric reductive…
Topological Frobenius reciprocity and invariant Hermitian forms.
In his article "Unitary Representations and Complex Analysis", David Vogan gives a characterization of the continuous invariant Hermitian forms defined on the compactly supported sheaf cohomology…
On the unitary globalization of cohomologically induced modules
Complex of twistor operators in symplectic spin geometry
For a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure), we construct a sequence consisting of differential operators using a symplectic…
Symplectic Dirac Operator and its Higher Spin Analogues
Symplectic Dirac operator is a symplectic counterpart of the classical Dirac operator known from Clifford analysis or Riemannian geometry. We introduce this operator and mention some of its…
Cohomological Induction on Generalized G-Modules to Infinite Dimensional Representations
Extensions and globalizations of Harish-Chandra modules are used to obtain a representation theory that includes the cases of non-compact type of irreducible representations studied in the Vogan…
The algebraic version of a conjecture by Vogan
In a recent manuscript, D.Vogan conjectures that four canonical globalizations of Harish-Chandra modules commute with certain n-cohomology groups. In this article we focus on the case of a complex…
Classification of 1st order symplectic spinor operators over contact projective geometries
Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds
Consider a flat symplectic manifold (M, ω), l ≥ 2, admitting a metaplectic structure. We prove that the symplectic twistor operator maps the eigenvectors of the symplectic Dirac operator, that are…
THE n-HOMOLOGY OF REPRESENTATIONS
The n-homology groups of a g-module provide a natural and fruitful extension of the concept of highest weight to the representation theory of a noncompact reductive Lie group. In this article we give…
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References

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