Cohomological Induction and Unitary Representations (PMS-45)

Knapp, Anthony W.; Vogan, David A.

doi:10.1515/9781400883936

Cited by 253 publications

(463 citation statements)

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“…The following wellknown results on the Harish-Chandra homomorphism and K-types are included in order to fix the precise values for Casimir operators needed later on, which indeed depend on the choices. The Harish-Chandra homomorphism is described as follows (see for example [7,IV. 7]).…”

Section: Casimir Elementsmentioning

confidence: 99%

On holomorphic projection for symplectic groups

Maurischat

2018

Journal of Number Theory

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Abstract. We define non-holomorphic Poincaré series of exponential type for symplectic groups Sp m (R) and continue them analytically in case m = 2 for the small weight (4, 4). For this we construct certain Casimir operators and study the spectral properties of their resolvents on L 2 (Γ\ Sp 2 (R)). Using the holomorphically continued Poincaré series, the holomorphic projection is described in terms of Fourier coefficients using Sturm's operator.

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Section: Casimir Elementsmentioning

confidence: 99%

On holomorphic projection for symplectic groups

Maurischat

2018

Journal of Number Theory

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“…When l is in the weakly fair range of De¢nition 3.4, Lemma 3.13 holds for general G, as a consequence of [KV,Lemma 8.39]. Outside the weakly fair range, the lemma (and hence Theorem 3.1b(iv)) are apparently new, although the proof is surprisingly simple.…”

Section: Annihilators and Associated Varietiesmentioning

confidence: 90%

“…The fair range is easily seen to contain the good range, and it's not too hard to see that the mediocre range contains the fair range (see [KV,Theorem 5.105]). The next lemma makes these ranges explicit in the U( p,q) setting (from which the containments become obvious).…”

Section: Annihilators and Associated Varietiesmentioning

confidence: 99%

“…The simple root a e i À e i 1 is said to be in the t-invariant of a n-standard tableau S if and only if n i 1 is strictly below n i in S; or, equivalently, if and only if i 1 is strictly below i in the underlying tableau of S. Now we isolate the relevant version of the translation principle. (See [KV,Chapter 7] and the references given there.) THEOREM 4.4.…”

Section: Annihilators and Associated Varietiesmentioning

confidence: 99%

“…By [KV,Theorem 8.2], X is irreducible. The results of [V1] imply that the ¢rst n 1 boxes of the underlying tableau of Ann(X) are characterized by applying sequences of wall-crossing translation functors to X.…”

Section: Annihilators and Associated Varietiesmentioning

confidence: 99%

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Trapa¹

2001

Compositio Mathematica

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Abstract. Vogan has conjectured that the cohomologically induced modules A q (l) in the weakly fair range exhaust all unitary representations of U(p,q) with certain kinds of real integral in¢nitesimal character. To prove a statement like this, it is essential to identify these modules among the set of all irreducible Harish-Chandra modules. Barbasch and Vogan have parametrized this latter set in terms of their annihilators and asymptotic supports (or, equivalently, associated varieties). In this paper, we identify the weakly fair A q (l) in this parametrization by combining known results about their asymptotic supports together with an explicit computation of their annihilators. In particular, this determines all vanishing and coincidences among the A q (l) in the weakly fair range, and gives the Langlands parameters of these modules.

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Component Groups of Centralizers of Nilpotents in Complex Symmetric Spaces

King

Noël

2000

Journal of Algebra

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Let G be the adjoint group of a simple Lie algebra , and let K C → Aut C be the complexified isotropy representation at the identity coset of the corresponding symmetric space. If e ∈ C is nilpotent, we consider the centralizer of e in K C . We show that the conjugacy classes of the component group of this centralizer can be described in terms generalizing the Bala-Carter classification of nilpotent orbits in the complexification of .

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Cohomological Induction and Unitary Representations (PMS-45)

Cited by 253 publications

References 0 publications

On holomorphic projection for symplectic groups

On holomorphic projection for symplectic groups

Untitled

Component Groups of Centralizers of Nilpotents in Complex Symmetric Spaces

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