03704nam 2200601 450 991078874880332120180613001305.01-4704-0422-2(CKB)3360000000465005(EBL)3114239(SSID)ssj0000973312(PQKBManifestationID)11552361(PQKBTitleCode)TC0000973312(PQKBWorkID)10960111(PQKB)10828997(MiAaPQ)EBC3114239(RPAM)13763500(PPN)195417097(EXLCZ)99336000000046500520041027h20052005 uy| 0engur|n|---|||||txtccrLocal zeta functions attached to the minimal spherical series for a class of symmetric spaces /Nicole Bopp, Hubert RubenthalerProvidence, Rhode Island :American Mathematical Society,[2005]©20051 online resource (250 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 821"Volume 174, number 821 (first of 4 numbers)."0-8218-3623-4 Includes bibliographical references (pages 227-230) and index.""Table of Contents""; ""Introduction""; ""Chapter 1. A Class of Real Prehomogeneous Spaces""; ""1.1. A class of graded algebras""; ""1.2. Root systems""; ""1.3. Complexification""; ""1.4. Highest root in Σ""; ""1.5. The first step for the descent""; ""1.6. The descent""; ""1.7. Generic elements in V[sup(+)]""; ""1.8. Structure of the regular graded algebra (g, H[sub(0)])""; ""1.9. Properties of the spaces E[sub(i,j)] (p, q)""; ""1.10. Normalization of the Killing form""; ""1.11. The relative invariant Î?[sub(0)]""; ""1.12. The case k = 0""; ""1.13. Properties of Î?[sub(0)]""""1.14. The polynomials Î?[sub(j)]""""Chapter 2. The Orbits of G in V[sup(+)]""; ""2.1. Representations of sl( 2, C)""; ""2.2. First reduction""; ""2.3. An involution which permutes the roots in E[sub(i,j)(+1,+1)""; ""2.4. Construction of elements interchanging λ[sub(i)] and λ[sub(j)]""; ""2.5. Quadratic forms""; ""2.6. The G-orbits for Type III""; ""2.7. The G-orbits for Type II""; ""2.8. Signature of the quadratic forms qx[sub(i)],x[sub(j)]""; ""2.9. Action of Z[sub(G)](I[sup(+)]) for Type I""; ""2.10. The Gâ€?orbits for Type I""; ""2.11. The classification""""4.2. Two diffeomorphisms""""4.3. Isomorphisms between g(1), g (â€?1), V[sup(+)]( l ) and V[sup(-)](â€?1)""; ""4.4. A first normalization and its consequence""; ""4.5. A second normalization and its consequence""; ""4.6. Integral formulas on V[sup(+)] and V[sup(-)]""; ""4.7. Fourier transform of a quadratic character""; ""4.8. A relation between T[sup(-)][sub(Ff)] and T[sup(+)][sub(f)]""; ""Chapter 5. Functional Equation of the Zeta Functionfor Type I and II""; ""5.1. Definition of the local Zeta functions""; ""5.2. Existence of a functional equation for (AN, V[sup(+)])""""6.5. Explicit functional equation for k = 0""Memoirs of the American Mathematical Society ;no. 821.Functions, ZetaSymmetric spacesFunctions, Zeta.Symmetric spaces.510 s515/.56Bopp Nicole1947-1521044Rubenthaler H(Hubert),MiAaPQMiAaPQMiAaPQBOOK9910788748803321Local zeta functions attached to the minimal spherical series for a class of symmetric spaces3759913UNINA