Some infinite dimensional representations of reductive groups with Frobenius maps

被引：14

作者：

Xi NanHua ^{[1
,2
]}

机构：

[1] Chinese Acad Sci, Inst Math, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2014年 / 57卷 / 06期

基金：

中国国家自然科学基金;

关键词：

infinite dimensional representation; reductive group; induced module; LINEAR-GROUPS; SHINTANI;

D O I：

10.1007/s11425-014-4818-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps. In particular, a few classical results of Steinberg and Deligne & Lusztig on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps.

引用

页码：1109 / 1120

页数：12

共 14 条

[1]

[Anonymous], 1984, ANN MATH STUDIES

[2] On a theorem of Shintani [J].

Bonnafé, C .

JOURNAL OF ALGEBRA, 1999, 218 (01) :229-245

[3] HOMOMORPHISM ABSTRACTS OF SIMPLE ALGEBRAIC GROUPS [J].

BOREL, A ;

TITS, J .

ANNALS OF MATHEMATICS, 1973, 97 (03) :499-571

[4]

Carter Roger W., 1993, FINITE GROUPS LIE TY

[5]

Curtis C. W., 1981, PURE APPL MATH, VII

[6]

Curtis Charles W., 1981, PURE APPL MATH, VI

[7] REPRESENTATIONS OF REDUCTIVE GROUPS OVER FINITE-FIELDS [J].

DELIGNE, P ;

LUSZTIG, G .

ANNALS OF MATHEMATICS, 1976, 103 (01) :103-161

[8] REPRESENTATIONS OF COXETER GROUPS AND HECKE ALGEBRAS [J].

KAZHDAN, D ;

LUSZTIG, G .

INVENTIONES MATHEMATICAE, 1979, 53 (02) :165-184

[9] LEFT CELLS IN WEYL GROUPS [J].

LUSZTIG, G .

LECTURE NOTES IN MATHEMATICS, 1983, 1024 :99-111

[10] CHARACTER SHEAVES .5. [J].

LUSZTIG, G .

ADVANCES IN MATHEMATICS, 1986, 61 (02) :103-155

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