Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0851.22022
Herb, Rebecca A.
Supertempered virtual characters. (English)
[J] Compos. Math. 93, No.2, 139-154 (1994). ISSN 0010-437X; ISSN 1570-5846/e

This paper proves a conjecture of {\it J. Arthur} [Acta Math. 171, 73-138 (1993; Zbl 0822.22011)] which identifies the supertempered virtual characters of a connected reductive $p$-adic group $G$. A tempered virtual character $\Theta$ is said to be ``supertempered'' if for every Cartan subgroup $T$ of $G$ and every $r > 0$ we have $$\sup_{t \in T'} |D_G (t) |^{1/2} |\Theta(t) |(1 + \sigma_*(t))^r < \infty,$$ where $\sigma_*$ measures polynomial growth on $G/Z_G$. Arthur used the $R$-group to describe certain combinations of irreducible characters which he predicted should be supertempered. The author not only proves this result but also shows that every supertempered virtual character is a linear combination of the ones suggested by Arthur.
[J.Repka (Toronto)]

MSC 2000:: *22E50 Repres. of Lie and linear algebraic groups over local fields
22E35 Analysis on p-adic Lie groups
20G05 Representation theory of linear algebraic groups
11S37 Langlands-Weil conjectures, nonabelian class field theory

Keywords: supertempered; reductive $p$-adic group; virtual character; Cartan subgroup; $R$-group; irreducible characters

Citations: Zbl 0822.22011

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]