Automorphic Forms And Shimura Varieties Of Pgsp(2) - Image 1

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World Scientific Publishing Company Automorphic Forms And Shimura Varieties Of Pgsp(2)

Name: Automorphic Forms And Shimura Varieties Of Pgsp(2)
Brand: World Scientific Publishing Company
Price: 47.72 GBP
Availability: InStock

Algebra

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Description

The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called “liftings.' This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2,≤) in SL(4, ≤). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum.Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations.To put these results in a general context, the book concludes with a technical introduction to Langlands' program in the area of automorphic representations. It includes a proof of known cases of Artin's conjecture.

Product Specifications

Brand: World Scientific Publishing Company
Format: hardcover
ASIN: 9812564039
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 16 August 2005
Listed Since: 12 February 2007

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World Scientific Publishing Company Automorphic Forms And Shimura Varieties Of Pgsp(2)

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