Singular Unitary Representations and Discrete Series for Indefinite Stiefel Manifolds U.
- 1st ed.
- 1 online resource (117 pages)
- Memoirs of the American Mathematical Society ; v.95 .
- Memoirs of the American Mathematical Society .
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 GL1. quarternionic case -- 2. orthogonal case -- References.
9781470408886
Semisimple Lie groups. Representations of groups. Harmonic analysis. Stiefel manifolds.