On the structure of generalized symmetric spaces of SLn(Fq)

被引：2

作者：

Buell, C. ^{[1
]}

Helminck, A. ^{[2
]}

Klima, V. ^{[3
]}

Schaefer, J. ^{[4
]}

Wright, C. ^{[5
]}

Ziliak, E. ^{[6
]}

机构：

[1] Fitchburg State Univ, Dept Math, Fitchburg, MA USA

[2] Univ Hawaii Manoa, Coll Nat Sci, Honolulu, HI 96822 USA

[3] Appalachian State Univ, Dept Math Sci, Boone, NC 28608 USA

[4] Dickinson Coll, Dept Math & Comp Sci, POB 1773, Carlisle, PA 17013 USA

[5] Jackson State Univ, Dept Math & Stat Sci, Jackson, MS USA

[6] Benedictine Univ, Dept Math & Computat Sci, Lisle, IL USA

来源：

COMMUNICATIONS IN ALGEBRA | 2017年 / 45卷 / 12期

关键词：

Finite fields; generalized symmetric space; special linear group; INVARIANT DISTRIBUTION VECTORS; SEMISIMPLE LIE-GROUPS; IRREDUCIBLE CHARACTERS; PRINCIPAL SERIES; INVOLUTIONS;

D O I：

10.1080/00927872.2017.1296458

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we extend previous results regarding SL2(k) over any finite field k by investigating the structure of the symmetric spaces for the family of special linear groups SLn(k) for any integer n>2. Specifically, we discuss the generalized and extended symmetric spaces of SLn(k) for all conjugacy classes of involutions over a finite field of odd or even characteristic. We characterize the structure of these spaces and provide an explicit difference set in cases where the two spaces are not equal.

引用

页码：5123 / 5136

页数：14

共 36 条

[1] Symmetric and alternate matrices in an arbitrary field, I [J].