Harmonic Analysis on Reductive Groups by Jeffrey Adams (auth.), Prof. William H. Barker, Prof. Paul

By Jeffrey Adams (auth.), Prof. William H. Barker, Prof. Paul J. Sally Jr. (eds.)

A convention on Harmonic research on Reductive teams used to be held at Bowdoin university in Brunswick, Maine from July 31 to August eleven, 1989. The acknowledged target of the convention was once to discover fresh advances in harmonic research on either actual and p-adic teams. It used to be the 1st convention because the AMS summer time Sym­ posium on Harmonic research on Homogeneous areas, held at Williamstown, Massachusetts in 1972, to hide neighborhood harmonic research on reductive teams in such element and to such an volume. whereas the Williamstown convention was once longer (three weeks) and a bit of broader (nilpotent teams, solvable teams, in addition to semisimple and reductive groups), the constitution and timeliness of the 2 conferences used to be remarkably comparable. this system of the Bowdoin convention consisted of 2 components. First, there have been six significant lecture sequence, each one along with numerous talks addressing these themes in harmonic research on genuine and p-adic teams which have been the focal point of extensive study throughout the earlier decade. those lectures all started at an introductory point and complex to the present country of analysis. Sec­ ond, there has been a sequence of unmarried lectures during which the audio system awarded an outline in their most recent research.

Show description

Read Online or Download Harmonic Analysis on Reductive Groups PDF

Similar analysis books

Grundzuege einer allgemeinen Theorie der linearen Integralgleichungen

This can be a pre-1923 old copy that used to be curated for caliber. caliber coverage was once performed on every one of those books in an try and eliminate books with imperfections brought via the digitization method. although we've made most sensible efforts - the books could have occasional blunders that don't abate the interpreting event.

Calculus of Residues

The issues contained during this sequence were amassed over decades with the purpose of delivering scholars and academics with fabric, the quest for which might in a different way occupy a lot precious time. Hitherto this centred fabric has in simple terms been obtainable to the very constrained public in a position to learn Serbian*.

Mathematik zum Studieneinstieg: Grundwissen der Analysis für Wirtschaftswissenschaftler, Ingenieure, Naturwissenschaftler und Informatiker

Studenten in den F? chern Wirtschaftswissenschaften, Technik, Naturwissenschaften und Informatik ben? tigen zu Studienbeginn bestimmte Grundkenntnisse in der Mathematik, die im vorliegenden Buch dargestellt werden. Es behandelt die Grundlagen der research im Sinne einer Wiederholung/Vertiefung des gymnasialen Oberstufenstoffes.

Additional resources for Harmonic Analysis on Reductive Groups

Sample text

We write (2-26) 23(x,y) for the block corresponding to the admissible pair (x, y). (2-27) Example: SL(2). The blocks of Example (2-22) are obtained as follows: (1) G = SL(2): (a) ~(o, Vo) is the block {PSe, 11"+, 11"_} of the trivial representation of SU(I, 1), (b) ~(too,vo) = {"';;~via,} for SU(2,O), (c) ~(-too,Vo) = {1I"~;~vial} for SU(O,2), (d) ~(o,to Vo) = {pso} for SU(I, 1). (2) G = PGL(2): (a) ~(o, V o) is the block {1I"d,PStrivial,PS8gn} containing the trivial representation of PU(I, 1), (b) ~(o,to Vo) = {ps+(2p)} for PU(I, 1), (c) ~(o, -to vo) = {ps-(2p)} for PU(I, 1), (d) 23(t oo, Vo) = {1I";;~vial} for PU(2,O).

5]) we may in fact choose y E vD, and furthermore require that int(y)lvH be a principal involution. Conjugating by vG we obtain the following Lemma (ef. 8]) which we use to compute weak endoscopic data. (4-3) Lemma. Fix v6 0 E vD, let Vo = int(V6 o), and letVK = (VG(8. (1) Given an elliptic element 8 with 11"(8') E vK, let vH r be the group generated by the centralizer vH of s = 11"(8) and v6 ' Then (8', VH r ) 0 is a set of weak endoscopic data, and every set of weak endoscopic data is equivalent to a set of this form.

We obtain a duality mapping from (g,kz ) modules to (Vg,Vky ) modules, and similarly dual blocks. Then Theorem (2-36) holds as stated. Note that we allow the E-groups Gf' and vGf' to vary independently. For example, let Gf' be an L-group, but let vGf' be a more general E-group. Then we see a block 23 of (g, /(z) modules is dual to a block of (Vg,Vk y ) modules for various covering groups of vG, including the trivial one. This flexibility will be important in §6. (2-46) Example: 8L(2). The block containing the trivial representation of SU(1, 1) is dual to the block of the trivial representation of PU(I, 1).

Download PDF sample

Rated 4.05 of 5 – based on 36 votes