Singular Unitary Representations and Discrete Series for Indefinite Stiefel Manifolds U.

Intro -- Contents -- 0. Introduction -- 1. Notation -- 1. θ-stable parabolic subalgebra -- 2. good range, fair range -- 3. cohomological parabolic induction -- 4. results from Zuckerman and Vogan -- 5. results from Harish-Chandra and Oshima-Matsuki -- 2. Main results -- 1. G = Spfaq) -- 2. main theorem for G = Sp(p,q) -- 3. G = U(p,q) -- 4. main theorem for G = U(p,q) -- 5. G = SO0(p,q) -- 6. main theorem for G = SOo( p,q) -- 7. list and figures of various conditions on parameters -- 8. remarks -- 3. Further notations and preliminary results -- 1. Jantzen-Zuckerman's translation functor -- 2. induction by stages -- 3. definition of A (λ[omitted] λ') -- 4. A (λ[omitted] λ') and derived functor modules -- 5. some symbols -- 4. Some explicit formulas on K multiplicities -- 1. preliminaries -- 2. some alternating polynomials -- 3. result in quaternionic case -- 4. result in complex case -- 5. result in real case -- 6. some auxiliary lemmas -- 7. proof for quarternionic case -- 8. proof for complex case -- 9. proof for real case -- 5. An alternative proof of the sufficiency for R[sup(s)][sub(q)](Cλ)≠ 0 -- 1. theorem: sufficient condition for R[sup(s)][sub(q)](Cλ)≠ 0 -- 2. key lemmas -- 3. proof of the combinatorial part -- 6. Proof of irreducibility results -- 1. irreducibility in the fair range -- 2. twisted differential operators -- 3. theorem -- 4. irreducibility result -- 5. Vogan's idea on the translation principle for Ay(l:g) -- 6. notations about GL{nz,C) and Sp(n,C) -- 7. definition of Cλ -- 8. verification of (6.5.4)(a) -- 9. verification of (6.5.4)(b) -- 10. verification of (6.5.4)(c) -- 11. proof of Corollary(6.4.1) -- 7. Proof of vanishing results outside the fair range -- 1. proof in complex case -- 2. vanishing result in quaternionic case -- 3. maximal parabolic case -- 4. general parabolic case -- 8. Proof of the inequivalence results.

1. quarternionic case -- 2. orthogonal case -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.