Celebratio Mathematica — Gross

From Gross–Zagier to GGP

Works connected to Dipendra Prasad

Filter the Bibliography List

year	title	people

			clear

W. T. Gan, B. H. Gross, and D. Prasad: “Symplectic local root numbers, central critical \( L \) values, and restriction problems in the representation theory of classical groups,” pp. 1–109 in Sur les conjectures de Gross et Prasad, I [The conjectures of Gross and Prasad, I]. Edited by W. T. Gan, B. H. Gross, D. Prasad, and J.-L. Waldspurger. Astérisque 346. Société Mathématique de France (Paris), 2012. MR 3202556 Zbl 1280.22019 ArXiv 0909.2999 incollection

It has been almost 20 years since two of us proposed a rather speculative approach to the problem of restriction of irreducible representations from \( \mathrm{SO}_n \) to \( \mathrm{SO}_{n-1} \) [Gross and Prasad 1992, 1994]. Our predictions depended on the Langlands parametrization of irreducible representations, using \( L \)-packets and \( L \)-parameters. Since then, there has been considerable progress in the construction of local \( L \)-packets, as well as on both local and global aspects of the restriction problem. We thought it was a good time to review the precise conjectures which remain open, and to present them in a more general form, involving restriction problems for all of the classical groups.

Wee Teck Gan	Related
Dipendra Prasad	Related

@incollection {key3202556m,
	AUTHOR = {Gan, Wee Teck and Gross, Benedict H.
		 and Prasad, Dipendra},
	TITLE = {Symplectic local root numbers, central
		 critical \$L\$ values, and restriction
		 problems in the representation theory
		 of classical groups},
	BOOKTITLE = {Sur les conjectures de {G}ross et {P}rasad,
		 {I} [The conjectures of {G}ross and
		 {P}rasad, {I}]},
	EDITOR = {Gan, Wee Teck and Gross, Benedict H.
		 and Prasad, Dipendra and Waldspurger,
		 Jean-Loup},
	SERIES = {Ast\'erisque},
	NUMBER = {346},
	PUBLISHER = {Soci\'et\'e Math\'ematique de France},
	ADDRESS = {Paris},
	YEAR = {2012},
	PAGES = {1--109},
	URL = {http://www.numdam.org/item/AST_2012__346__1_0/},
	NOTE = {ArXiv:0909.2999. MR:3202556. Zbl:1280.22019.},
	ISSN = {0303-1179},
	ISBN = {9782856293485},
}