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A01=Dihua Jiang
A01=Lei Zhang
A01=Zhilin Luo
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Author_Dihua Jiang
Author_Lei Zhang
Author_Zhilin Luo
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Harmonic Analysis and Gamma Functions on Symplectic Groups

English

By (author): Dihua Jiang Lei Zhang Zhilin Luo

Over a p-adic local field F of characteristic zero, we develop a new type of harmonic analysis on an extended symplectic group G = Gm × Sp2n. It is associated to the Langlands ?-functions attached to any irreducible admissible representations ? ? ? of G(F) and the standard representation ? of the dual group G?(C), 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 ??(?s) (a product of n + 1 certain abelian ?-functions). Our work on GL1(F) plays an indispensable role in the development of our work on G(F). 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. See more
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A01=Dihua JiangA01=Lei ZhangA01=Zhilin LuoAge Group_UncategorizedAuthor_Dihua JiangAuthor_Lei ZhangAuthor_Zhilin Luoautomatic-updateCategory1=Non-FictionCategory=PBFCategory=PBMWCOP=United StatesDelivery_Delivery within 10-20 working daysLanguage_EnglishPA=AvailablePrice_€50 to €100PS=Activesoftlaunch
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Product Details
  • Weight: 272g
  • Dimensions: 178 x 254mm
  • Publication Date: 31 May 2024
  • Publisher: American Mathematical Society
  • Publication City/Country: United States
  • Language: English
  • ISBN13: 9781470469078

About Dihua JiangLei ZhangZhilin Luo

Dihua Jiang University of Minnesota Minneapolis MN.Zhilin Luo University of Chicago IL.Lei Zhang National University of Singapore Singapore.

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