Local zeta functions attached to the minimal spherical series for a class of symmetric spaces / / Nicole Bopp, Hubert Rubenthaler

• Autore: Bopp Nicole <1947->
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [2005]; ©2005
• Descrizione fisica: 1 online resource (250 p.)
• Disciplina: 510 s; 515/.56
• Soggetto topico: Functions, Zeta; Symmetric spaces
• Soggetto genere / forma: Electronic books.
• Persona (resp. second.): RubenthalerH (Hubert)
• Note generali: "Volume 174, number 821 (first of 4 numbers)."
• Nota di bibliografia: Includes bibliographical references (pages 227-230) and index.
• Nota di contenuto: ""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""
• Titolo autorizzato: Local zeta functions attached to the minimal spherical series for a class of symmetric spaces
• ISBN: 1-4704-0422-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910480099303321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; no. 821.