Fixed-point group conjugacy classes of unipotent elements in low-dimensional symmetric spaces of special linear groups over a finite field

被引：1

作者：

Buell, Catherine ^{[1
]}

Helminck, Aloysius ^{[2
]}

Klima, Vicky ^{[3
]}

Schaefer, Jennifer ^{[4
]}

Wright, Carmen ^{[5
]}

Ziliak, Ellen ^{[6
]}

机构：

[1] Fitchburg State Univ, Dept Math, 160 Pearl St, Fitchburg, MA 01420 USA

[2] Univ Hawaii Manoa, Coll Nat Sci, 2565 McCarthy Mall, Honolulu, HI 96822 USA

[3] Appalachian State Univ, Dept Math Sci, 121 Bodenheimer Dr Boone, North Carolina, NC 28608 USA

[4] Dickinson Coll, Dept Math & Comp Sci, 28 North Coll St, Carlisle, PA 17013 USA

[5] Jackson State Univ, Dept Math & Stat Sci, POB 17610, Jackson, MS USA

[6] Benedictine Univ, Dept Math & Computat Sci, Birck Hall Sci Room 1355700 Coll Rd, Lisle, IL 60532 USA

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2024年 / 23卷 / 09期

关键词：

Unipotent; generalized symmetric space; special linear group; orbits; finite fields; INVOLUTIONS; SL(N; K);

D O I：

10.1142/S0219498824501421

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we characterize and classify the orbits of the fixed-point group on the unipotent elements of the generalized symmetric spaces for inner involutions of SL3(k) and SL4(k) where k is a finite field of odd characteristic. We provide some generalized results for SLn(k).

引用

页数：27

共 22 条

[1]

Aliakseyeu R., COUNTING GEN EXTENDE

[2]

[Anonymous], 1985, Algebraic groups and related topics, P525

[3]

Berger M., 1957, Ann. Sci. Ecole Norm. Sup.(3), P85, DOI [10.24033/asens.1054, DOI 10.24033/ASENS.1054]

[4] On orbit closures of symmetric subgroups in flag varieties [J].

Brion, M ;

Helminck, AG .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2000, 52 (02) :265-292

[5] Classifying the orbits of the generalized symmetric spaces for SL2(Fq) [J].

Buell, C. ;

Helminck, A. ;

Klima, V. ;

Schaefer, J. ;

Wright, C. ;

Ziliak, E. .

COMMUNICATIONS IN ALGEBRA, 2020, 48 (04) :1744-1757

[6]

Buell C, 2017, NOTE MAT, V37, P1, DOI 10.1285/i15900932v37n2p1

[7] On the structure of generalized symmetric spaces of SLn(Fq) [J].

Buell, C. ;

Helminck, A. ;

Klima, V. ;

Schaefer, J. ;

Wright, C. ;

Ziliak, E. .

COMMUNICATIONS IN ALGEBRA, 2017, 45 (12) :5123-5136

[8]

Buell C., 2018, Advances in the Mathematical Sciences, P69, DOI [10.1007/978-3-319-98684-5, DOI 10.1007/978-3-319-98684-5]

[9]

Cartan E., 1926, Bull. Soc. Math. France, V54, P214, DOI [10.24033/bsmf.1105, DOI 10.24033/BSMF.1105]

[10]

Cartan E., 1927, Bull. Soc. Math. France, V55, P114, DOI DOI 10.24033/BSMF.1113

← 1 2 3 →