Multiplicity one theorems for GSp(k, 2n) and O(k, n), where k is a finite field

Mina Teicher

doi:10.1016/0021-8693(87)90098-6

Multiplicity one theorems for GSp(k, 2n) and O(k, n), where k is a finite field

Mina Teicher

Department of Mathematics

Institute for Advanced Studies

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The aim of this paper is to give a result similar to the following result of Gelfand and Graev [ 11: Let U be a maximal unipotent subgroup of a finite Chevalley group G. For each nondegenerate x, the induced representation IndgX is multiplicity-free. In part I we shall prove a theorem of that kind for Gsp(2n, k), and in Part II for O(n, k). These theorems were conjectured and given to me by I. Piatetski Shapiro.

Original language	English
Pages (from-to)	436-465
Number of pages	30
Journal	Journal of Algebra
Volume	107
Issue number	2
DOIs	https://doi.org/10.1016/0021-8693(87)90098-6
State	Published - May 1987

Bibliographical note

Funding Information:
in part by the NSF

Funding

in part by the NSF

Funders
National Science Foundation

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10.1016/0021-8693(87)90098-6

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title = "Multiplicity one theorems for GSp(k, 2n) and O(k, n), where k is a finite field",

abstract = "The aim of this paper is to give a result similar to the following result of Gelfand and Graev [ 11: Let U be a maximal unipotent subgroup of a finite Chevalley group G. For each nondegenerate x, the induced representation IndgX is multiplicity-free. In part I we shall prove a theorem of that kind for Gsp(2n, k), and in Part II for O(n, k). These theorems were conjectured and given to me by I. Piatetski Shapiro.",

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N2 - The aim of this paper is to give a result similar to the following result of Gelfand and Graev [ 11: Let U be a maximal unipotent subgroup of a finite Chevalley group G. For each nondegenerate x, the induced representation IndgX is multiplicity-free. In part I we shall prove a theorem of that kind for Gsp(2n, k), and in Part II for O(n, k). These theorems were conjectured and given to me by I. Piatetski Shapiro.

AB - The aim of this paper is to give a result similar to the following result of Gelfand and Graev [ 11: Let U be a maximal unipotent subgroup of a finite Chevalley group G. For each nondegenerate x, the induced representation IndgX is multiplicity-free. In part I we shall prove a theorem of that kind for Gsp(2n, k), and in Part II for O(n, k). These theorems were conjectured and given to me by I. Piatetski Shapiro.

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Multiplicity one theorems for GSp(k, 2n) and O(k, n), where k is a finite field

Abstract

Bibliographical note

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