03488nam 2200613 450 991048069760332120180731043559.01-4704-0888-0(CKB)3360000000464646(EBL)3113770(SSID)ssj0000889213(PQKBManifestationID)11493932(PQKBTitleCode)TC0000889213(PQKBWorkID)10876587(PQKB)11023043(MiAaPQ)EBC3113770(PPN)195413458(EXLCZ)99336000000046464620140902h19921992 uy 0engur|n|---|||||txtccrSingular unitary representations and discrete series for indefinite Stiefel manifolds U(p,q;F)/U(p-m,q;F) /Toshiyuki KobayashiProvidence, Rhode Island :American Mathematical Society,1992.©19921 online resource (117 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 95, Number 462"January 1992, Volume 95, Number 462 (end of volume)."0-8218-2524-0 Includes bibliographical references.""Contents""; ""0. Introduction""; ""1. Notation""; ""1. Î?-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""""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""Memoirs of the American Mathematical Society ;Volume 95, Number 462.Semisimple Lie groupsRepresentations of groupsHarmonic analysisStiefel manifoldsElectronic books.Semisimple Lie groups.Representations of groups.Harmonic analysis.Stiefel manifolds.512/.55Kobayashi Toshiyuki1962-919086MiAaPQMiAaPQMiAaPQBOOK9910480697603321Singular unitary representations and discrete series for indefinite Stiefel manifolds U(p,q;F)2061336UNINA