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Harmonic analysis and gamma functions on symplectic groups / Dihua Jiang, Zhilin Luo, Lei Zhang

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 295, number 1473 (March 2024)Publisher: Providence, RI : American Mathematical Society, March 2024Description: vii, 89 SeitenISBN:
  • 9781470469078
Subject(s): Additional physical formats: 9781470477738 | Erscheint auch als: Harmonic analysis and gamma functions on symplectic groups. Online-Ausgabe Providence, RI : American Mathematical Society, 2024. 1 Online-Ressource (vii, 89 Seiten)DDC classification:
  • 516/.12 23/eng/20240731
MSC: MSC: 11F66 | 43A32 | 46S10 | 11F70 | 22E50 | 43A80 | 11F66LOC classification:
  • QA403
Summary: Keywords: Invariant distribution, Fourier operator, Langlands local gamma function and L-function, representation, symplectic group, p-adic local fieldSummary: "Over a adic local field F of characteristic zero, we develop a new type of harmonic analysis on an extended symplectic group . It is associated to the Langlands-functions attached to any irreducible admissible representations of and the standard representation of the dual group , and confirms a series of the conjectures in the local theory of the Braverman-Kazhdan proposal (Braverman and Kazhdan, 2000) for the case under consideration. Meanwhile, we develop a new type of harmonic analysis on GL1(F), which is associated to a-function (a product of n 1 certain abelian -functions). Our work on plays an indispensable role in the development of our work on . These two types of harmonic analyses both specialize to the well-known local theory developed in Tate's thesis (Tate, 1950) when n = 0. The approach is to use the compactification of Sp2n in the Grassmannian variety of Sp4n, with which we are able to utilize the well developed local theory of Piatetski-Shapiro and Rallis (1986) and many other works) on the doubling local zeta integrals for the standard L-functions of Sp2n. The method can be viewed as an extension of the work of Godement-Jacquet (1972) for the standard L-function of GLn and is expected to work for all classical groups. We will consider the Archimedean local theory and the global theory in our future work"--PPN: PPN: 1891814109
Holdings
Item type Home library Shelving location Call number Status
Institutsbestand Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 57 c-295.2024,1473 Nicht ausleihbar
Total holds: 0
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