Get Harmonic Analysis on Reductive, p-adic Groups PDF

By Robert S. Doran, Paul J., Jr. Sally, Loren Spice

ISBN-10: 0821849859

ISBN-13: 9780821849859

This quantity includes the lawsuits of the AMS designated consultation on Harmonic research and Representations of Reductive, $p$-adic teams, which used to be hung on January sixteen, 2010, in San Francisco, California. one of many unique guiding philosophies of harmonic research on $p$-adic teams used to be Harish-Chandra's Lefschetz precept, which instructed a robust analogy with genuine teams. From this starting, the topic has built a shocking number of instruments and purposes. to say quite a few, Moy-Prasad's improvement of Bruhat-Tits idea relates research to team activities on in the neighborhood finite polysimplicial complexes; the Aubert-Baum-Plymen conjecture relates the neighborhood Langlands conjecture to the Baum-Connes conjecture through a geometrical description of the Bernstein spectrum; the $p$-adic analogues of classical symmetric areas play an important position in classifying representations; and personality sheaves, initially constructed via Lusztig within the context of finite teams of Lie sort, even have connections to characters of $p$-adic teams. The papers during this quantity current either expository and study articles on those and similar themes, proposing a extensive photo of the present cutting-edge in $p$-adic harmonic research. The suggestions are liberally illustrated with examples, frequently acceptable for an upper-level graduate scholar in illustration conception or quantity thought. The concrete case of the two-by-two precise linear workforce is a continuing touchstone

Show description

Read or Download Harmonic Analysis on Reductive, p-adic Groups PDF

Best algebra & trigonometry books

New PDF release: Kodaira-Spencer Maps in Local Algebra

The monograph contributes to Lech's inequality - a 30-year-old challenge of commutative algebra, originating within the paintings of Serre and Nagata, that relates the Hilbert functionality of the whole house of an algebraic or analytic deformation germ to the Hilbert functionality of the parameter house. A weakened model of Lech's inequality is proved utilizing a development that may be regarded as an area analog of the Kodaira-Spencer map identified from the deformation conception of compact complicated manifolds.

Noncommutative Geometry and Global Analysis: Conference in - download pdf or read online

This quantity represents the court cases of the convention on Noncommutative Geometric equipment in international research, held in honor of Henri Moscovici, from June 29-July four, 2009, in Bonn, Germany. Henri Moscovici has made a couple of significant contributions to noncommutative geometry, international research, and illustration idea.

Additional info for Harmonic Analysis on Reductive, p-adic Groups

Example text

Springer, A purity result for fixed point varieties in flag manifolds, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 (1984), no. 2, 271–282. Tonny A. Springer and Robert Steinberg, Conjugacy classes, Seminar on Algebraic Groups and Related Finite Groups. (Held at The Institute for Advanced Study, Princeton, NJ, 1968/69) (A. Borel and R. ), Lecture Notes in Mathematics, vol. 131, Springer– Verlag, Berlin, 1970, pp. 167–266. Tonny A. Springer, Linear Algebraic Groups, Second Edition, Modern Birkh¨ auser Classics, Birkh¨ auser, Boston, 2009.

G(Λ ) := q −1/2 Λ(− )r (X 2 ). 4], Waldspurger works with an additive character ψ of depth 0. 4]. 2], where our G(Λ ) is denoted by G (Φ). 2. measdΛ z (Rθ ) = and H(Λ , kθ ) = ⎧ ⎨q r+1 , θ= ⎩ θ= q r+1/2 , ⎧ ⎨(−1)r+1 , θ= ⎩ θ= G(Λ ), 31 13 ; . 3], this formula agrees with the one given in [42, p. 1235]. Proof. Note that H(Λ , kθ ) is just what is called H(Λ , Q) in [46, p. 11], where Q = Normθ is the norm form on kθ . 2 loc. cit. shows that the choice does not matter). For definiteness, we take the lattice to be Rθ .

In the first example above, X is nilpotent, so the corresponding coset does not correspond to an unrefined minimal K-type. , the filtration associated to the point xC ). If r ∈ Z, then every coset in the quotient space gxC ,−r /gxC ,(−r)+ has the form −r Xβsplit +gxC ,(−r)+ . As before, we may take β to lie in f× . Similarly, if r ∈ Z+ 12 , then every coset in the quotient space gxC ,−r /gxC ,(−r)+ either contains a nilpotent element or has the form (up to conjugation by GxC ) − r Xβθ,η + gxC ,(−r)+ , where θ ∈ { , } and η ∈ {1, }.

Download PDF sample

Harmonic Analysis on Reductive, p-adic Groups by Robert S. Doran, Paul J., Jr. Sally, Loren Spice

by John

Rated 4.92 of 5 – based on 17 votes