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Automorphic Representations of Low Rank Groups [Hardcover]

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Item description for Automorphic Representations of Low Rank Groups by Yuval Z. Flicker...

The area of automorphic representations and their local components (i.e. admissible representations) is a natural continuation of the main research of the 19th and 20th centuries studies in number theory and modular forms. A guiding principle is a reciprocity law that would relate these infinite-dimensional representations of a reductive group with finite dimensional representations of the Galois group of the number field. Simple relations on the Galois side would have deep counterpart relations on the automorphic side, called ``liftings''. These lifting relations are accessible purely on the automorphic side by using several analytic techniques. This monograph concentrates on one initial yet deep example, of the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of SL(2), namely its isomorphism with SO(3). It applies one technique, i.e. comparison of the trace formula with the twisted trace formula, both stabilized. All aspects of the technique are discussed in an elementary way: * The "Fundamental Lemma", relating orbital integrals of spherical functions; * Comparison of trace formulae is greatly simplified by using "regular" test functions; * The "lifting" is stated and proved by means of Harish--Chandra character relations. This permits an intrinsic definition of partition of the automorphic representations of SL(2) into packets, proving the Multiplicity One Theorem and Rigidity Theorem for SL(2), as well as determining the self-contragredient representations of PGL(3). This research monograph will benefit an audience of graduate students and researchers in the areas of number theory, algebra, and representation theory.



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Item Specifications...


Studio: World Scientific Publishing Company
Pages   485
Est. Packaging Dimensions:   Length: 1" Width: 6.25" Height: 9.25"
Weight:   1.9 lbs.
Binding  Hardcover
Release Date   Jun 27, 2006
Publisher   World Scientific Publishing Company
ISBN  9812568034  
ISBN13  9789812568038  


Availability  0 units.


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1Books > Subjects > Nonfiction > Politics > General
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3Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Algebra > General
4Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Group Theory
5Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Number Theory
6Books > Subjects > Science > Mathematics > General
7Books > Subjects > Science > Mathematics > Pure Mathematics > Algebra > General
8Books > Subjects > Science > Mathematics > Pure Mathematics > Group Theory
9Books > Subjects > Science > Mathematics > Pure Mathematics > Number Theory



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