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Singular Unitary Representations and Discrete Series for indefinite Stiefel manifolds U
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Interesting classes of (g,K)-modules are often described naturally in terms of cohomologically induced representations in various settings, such as unitary highest weight modules, the theory of dual reductive pairs, discrete series for semisimple theory of dual reductive pairs, discrete series for semisimple symmetric spaces, etc. These have been stimulating the study of algebraic properties of derived functor modules. Now an almost satisfactory theory on derived functor modules, including a functorial property about unitarizability, has been developed in the "good" range of parameters, though...
Interesting classes of (g,K)-modules are often described naturally in terms of cohomologically induced representations in various settings, such as unitary highest weight modules, the theory of dual reductive pairs, discrete series for semisimple theory of dual reductive pairs, discrete series for semisimple symmetric spaces, etc. These have been stimulating the study of algebraic properties of derived functor modules. Now an almost satisfactory theory on derived functor modules, including a functorial property about unitarizability, has been developed in the "good" range of parameters, though some subtle problems still remain. This work treats a relatively singular part of the unitary dual of pseudo-orthogonal groups U(p,q;F) over F = R, C and H. These representations arise from discrete series for indefinite Stiefel manifolds U(p,q;F)/U(p - m,q,F)(2m4p). Thanks to the duality theorem between d-module construction and Zuckerman's derived functor modules (ZDF-modules), these discrete series are naturally described in terms of ZF-modules with possibly singular parameters. The author's approach is algebraic and covers some parameters wandering outside the canonical Weyl chamber.
Table of contents:
Notation; Main results; Further notations and preliminary results; Some explicit formulas on K multiplicities; An alternative proof of the sufficiency fo Rsq(C *l)=O; Proof of irreducibility results; Proof of vanishing results outside the fair range; Proof of the inequivalence results outside the fair range; Proof of the inequivalence results.
This work treats a relatively singular part of the unitary dual of pseudo-orthogonal groups U(p,q;F) over F = R, C and H. These representations arise from discrete series for indefinite Stiefel manifolds U(p,q;F)/U(p - m,q,F)(2m4p). Thanks to the duality theorem between d-module construction and Zuckerman's derived functor modules (ZDF-modules), these discrete series are naturally described in terms of ZF-modules with possibly singular parameters. The author's approach is algebraic and covers some parameters wandering outside the canonical Weyl chamber.
Table of contents:
Notation; Main results; Further notations and preliminary results; Some explicit formulas on K multiplicities; An alternative proof of the sufficiency fo Rsq(C *l)
This work treats a relatively singular part of the unitary dual of pseudo-orthogonal groups U(p,q;F) over F = R, C and H. These representations arise from discrete series for indefinite Stiefel manifolds U(p,q;F)/U(p - m,q,F)(2m