Matching of Orbital Integrals on GL(4) and GSp(2)

ISBN-10: 0821809598
ISBN-13: 9780821809594
Category: Mathematics
Pages: 112
Language: English
Published: 1999
Publisher: American Mathematical Soc.
Author: Yuval Zvi Flicker

Description

The trace formula is the most powerful tool currently available to establish liftings of automorphic forms, as predicted by Langlands principle of functionality. The geometric part of the trace formula consists of orbital integrals, and the lifting is based on the fundamental lemma. The latter is an identity of the relevant orbital integrals for the unit elements of the Hecke algebras. This volume concerns a proof of the fundamental lemma in the classically most interesting case of Siegel modular forms, namely the symplectic group $Sp(2)$. These orbital integrals are compared with those on $GL(4)$, twisted by the transpose inverse involution. The technique of proof is elementary. Compact elements are decomposed into their absolutely semi-simple and topologically unipotent parts also in the twisted case; a double coset decomposition of the form $H\backslash G/K$--where H is a subgroup containing the centralizer--plays a key role.

Get the book

Other editions

Matching of Orbital Integrals on Gl(4) and Gsp(2)
- 2014-09-11
- 112 pages
- Paperback
- Oxford University Press, USA

Similar books

Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds
By Rainer Weissauer
... II. 25. Deligne P., Kazhdan D., Vigneras M.-F. Representations des algebres centrales simples p-adiques, Representations des groupes r ́eductifs sur un corps local. Hermann, 1984. 26. Flicker Y.F. Matching of orbital integrals on Gl(4) and ...
$Invariant Representations of $\mathrm {GSp}(2)$ under Tensor Product with a Quadratic Character$

Invariant Representations of $\mathrm {GSp}(2)$ under Tensor Product with a Quadratic Character
By Ping-Shun Chan
... Matching of orbital integrals on GL(4) and GSp(2). Mem. Amer. Math. Soc. No. 655 (1999). MR1468177 (99g:11068) , Lifting automorphic forms of PGSp(2), Part I. in Automorphic forms and Shimura varieties of PGSp(2). World Scientific (2005) ...
The Fundamental Lemma for the Shalika Subgroup of $GL(4)$
By Solomon Friedberg, Herve Jacquet
... for the trace formula at hand. The orbital integral on GSp(4) is of Kloosterman type, while the orbital integral on GL(4) is a new sort of relative Kloosterman integral. This matching is the first crucial step in establishing the ...
Contributions to Automorphic Forms, Geometry, and Number Theory: A Volume in Honor of Joseph Shalika
By Freydoon Shahidi, Dinakar Ramakrishnan, Haruzo Hida
CHAPTER 22 BEYOND ENDOSCOPY By ROBERT P. LANGLANDS Ya tutarsa – Nasreddin Hoca Dedicated to Joseph Shalika on the occasion of his sixtieth birthday Informal reference . There is available at http://SunSITE.UBC.
Automorphic Forms and Shimura Varieties of PGSp (2)
By Yuval Zvi Flicker
... for U(3), J. Analyse Math. 52 (1989), 39–52; IV. Characters, genericity, and multiplicity one for U(3), J. Analyse Math. 94 (2004), 1-15. Y. Flicker, Matching of orbital integrals on GL(4) and GSp(2), Mem. Amer. Math. Soc. no. 655, vol ...
Sobolev Met Poincare
By Pekka Koskela, Piotr Hajłasz
... Matching of orbital integrals on GL(4) and GSp(2), 1999 Wancheng Sheng and Tong Zhang, The Riemann problem for the transportation equations in gas dynamics, 1999 L. C. Evans and W. Gangbo, Differential equations methods for the Monge ...
Invariant Measures for Unitary Groups Associated to Kac-Moody Lie Algebras
By Doug Pickrell
... 2000 M. A. Dickmann and F. Miraglia, Special groups: Boolean-theoretic methods in the theory of quadratic forms, ... 1999 B. H. Bowditch, Treelike structures arising from continua and convergence groups, 1999 (Continued in the back ...
Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps
By Sjoerd M. Verduyn Lunel, Roger D. Nussbaum
Ergodic theory and dynamical systems to ROBERT F. WILLIAMS, Department of Mathematics, University of Texas at Austin, Austin, TX 78712-1082; e-mail: bobQ math. utexas. edu Real and harmonic analysis and geometric partial differential ...
Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems
By Hasna Riahi
... [(2,C)^* and combinatorial identities, 1999 Lindsay N. Childs, Cornelius Greither, David J. Moss, Jim Sauerberg, and ... Conjugacy of Alt5 and SL(2,5) subgroups of E8(C), 1998 Dikran Dikranjan and Dmitri Shakhmatov, Algebraic structure of ...
Inverse Invariant Theory and Steenrod Operations
By Mara D. Neusel
... Matching of orbital integrals on GL(4) and GSp(2), 1999 Wancheng Sheng and Tong Zhang, The Riemann problem for the transportation equations in gas dynamics, 1999 L. C. Evans and W. Gangbo, Differential equations methods for the Monge ...