Introduction to Harmonic Analysis on Reductive P-adic by Allan G. Silberger

By Allan G. Silberger

Based on a chain of lectures given via Harish-Chandra on the Institute for complicated research in 1971-1973, this publication offers an creation to the speculation of harmonic research on reductive p-adic groups.

Originally released in 1979.

The Princeton Legacy Library makes use of the most recent print-on-demand know-how to back make on hand formerly out-of-print books from the celebrated backlist of Princeton college Press. those variants safeguard the unique texts of those vital books whereas offering them in sturdy paperback and hardcover variants. The aim of the Princeton Legacy Library is to drastically raise entry to the wealthy scholarly historical past present in the millions of books released by means of Princeton collage Press in view that its founding in 1905.

Show description

Read or Download Introduction to Harmonic Analysis on Reductive P-adic Groups. (MN-23): Based on lectures by Harish-Chandra at The Institute for Advanced Study, 1971-73 (Mathematical Notes) PDF

Similar symmetry and group books

The Isomorphism Problem in Coxeter Groups

The e-book is the 1st to offer a entire evaluation of the options and instruments presently getting used within the research of combinatorial difficulties in Coxeter teams. it truly is self-contained, and obtainable even to complex undergraduate scholars of arithmetic. the first objective of the publication is to spotlight approximations to the tough isomorphism challenge in Coxeter teams.

GROUPS - CANBERRA 1989. ISBN 3-540-53475-X.

Berlin 1990 Springer. ISBN 3-540-53475-X. Lecture Notes in arithmetic 1456. octavo. ,197pp. , unique published wraps. close to tremendous, moderate mark on entrance.

Extra resources for Introduction to Harmonic Analysis on Reductive P-adic Groups. (MN-23): Based on lectures by Harish-Chandra at The Institute for Advanced Study, 1971-73 (Mathematical Notes)

Sample text

1 T(6U(h) 2 ~(h) 2 a(h- )'(). First we shall show that = fcy(xh 1,xyh2 )d1 x -1 = f G y(xh1,xyh2 )6G (x)drx = fcy(x,xh~ 1 yh2 )6i(xh; 1 )drx -1 = 6 c(hl)'(O(hl yh2). Next, using Lemma 1. 7. 6 and the first part of this lemma, we have and 55 Our reformulation follows immediately from Theorem 1. 2 and Lemma 1. 9. 3 together with the obvious fact that yt- y 0 is surjective on c:(G : E). Theorem 1. 4. for all h 'J Let = (h1,h2 ) e "H- be the space of all E-distributions There exists an injective linear and y 0 e mapping of "IO(ir1, ir2 ) into TO on G such that J.

K1lK I -.... 1. Thus, in the special case in which, in effect, we induce from H = (1), the theorem is true. To extend the argument to the case of general H and cr, we first use Lemma 1. 7. ). ). if = 0 for all ct Lemma 1. 6, P(ct) E 1l 1 _.!. _.! such that P(ct) = 0 if and only (P as in Lemma 1. 7. 5). By 1 = P(cS~z(h)o;a(h)cr(h)p(h)ct) tl1 (H,a\-C V-~, 1£1 (H, cr)- V- 1 corresponds to an element of l if cpe may be regarded as a subrepresentation of I then for all ct e 1e.

To prove the surjectivity it suffices to show that, C an arbitrarily small open compact subset of G and there exists a e c 00c (G : V) such that Pa = c- 1CilHCK. /J. /J e 1e. /J (xh)d 1h Pa(x) = 0, x ( CH. This implies the lemma. Lemma 1. 7. 6. and a e C 00 (G : V) c .! -1 P(P(h)a) = 6 2 (h)6G(h) 2 P(a(h )a). For every h e H 1 Proof. P(p(h)a)(x) = JHx(h' )2 a(h' )(p(h)a)(xh' )dth' Theorem 1. 7. 7. 1 = JHx(h' )2 a(h' )a(xh' h)d h' l = JH x(h' )2 a(h' )a(xh'h)6- 1 (h' )d h' 1 r Let G, H and a be as before.

Download PDF sample

Rated 4.48 of 5 – based on 28 votes