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

Von:

Jiang, Dihua [VerfasserIn]

Mitwirkende(r):

Resource type: Ressourcentyp: BuchBuchSprache: Englisch Reihen: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 295, number 1473 (March 2024)Verlag: Providence, RI : American Mathematical Society, March 2024Beschreibung: vii, 89 SeitenISBN:

9781470469078

Schlagwörter:

Andere physische Formen: 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-Klassifikation:

516/.12 23/eng/20240731

MSC: MSC: 11F66 | 43A32 | 46S10 | 11F70 | 22E50 | 43A80 | 11F66LOC-Klassifikation:

QA403

Zusammenfassung: Keywords: Invariant distribution, Fourier operator, Langlands local gamma function and L-function, representation, symplectic group, p-adic local fieldZusammenfassung: "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

Exemplare ( 1 )

Exemplare
Medientyp	Heimatbibliothek	Standort	Signatur	Status
Institutsbestand	Fachbibliothek Mathematik	Bibliothek / frei aufgestellt	Z 57 c-295.2024,1473	Nicht ausleihbar

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