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NORMALIZER OF THE CHEVALLEY GROUP OF TYPE E-7. / Vavilov, N. A.; Luzgarev, A. Yu.

In: St. Petersburg Mathematical Journal, Vol. 27, No. 6, 12.2016, p. 899-921.

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

Harvard

Vavilov, NA & Luzgarev, AY 2016, 'NORMALIZER OF THE CHEVALLEY GROUP OF TYPE E-7', St. Petersburg Mathematical Journal, vol. 27, no. 6, pp. 899-921. https://doi.org/10.1090/spmj/1426

APA

Vavilov, N. A., & Luzgarev, A. Y. (2016). NORMALIZER OF THE CHEVALLEY GROUP OF TYPE E-7. St. Petersburg Mathematical Journal, 27(6), 899-921. https://doi.org/10.1090/spmj/1426

Vancouver

Vavilov NA, Luzgarev AY. NORMALIZER OF THE CHEVALLEY GROUP OF TYPE E-7. St. Petersburg Mathematical Journal. 2016 Dec;27(6):899-921. https://doi.org/10.1090/spmj/1426

Author

Vavilov, N. A. ; Luzgarev, A. Yu. / NORMALIZER OF THE CHEVALLEY GROUP OF TYPE E-7. In: St. Petersburg Mathematical Journal. 2016 ; Vol. 27, No. 6. pp. 899-921.

BibTeX

@article{f3ee47898bc0444c867cf5ae64271113,
title = "NORMALIZER OF THE CHEVALLEY GROUP OF TYPE E-7",
abstract = "The simply connected Chevalley group G(E-7, R) of type E-7 is considered in the 56-dimensional representation. The main objective is to prove that the following four groups coincide: the normalizer of the elementary Chevalley group E(E-7, R), the normalizer of the Chevalley group G(E-7, R) itself, the transporter of E(E-7, R) into G(E-7, R), and the extended Chevalley group G (E-7, R). This holds over an arbitrary commutative ring R, with all normalizers and transporters being calculated in GL(56, R). Moreover, G (E-7, R) is characterized as the stabilizer of a system of quadrics. This last result is classically known over algebraically closed fields, here it is proved that the corresponding group scheme is smooth over Z, which implies that it holds over arbitrary commutative rings. These results are a key step in a subsequent paper, devoted to overgroups of exceptional groups in minimal representations.",
keywords = "Chevalley groups, elementary subgroups, minimal modules, invariant forms, decomposition of unipotents, root elements, highest weight orbit, REPRESENTATIONS, OVERGROUPS, группа Шевалле, элементарная подгруппа, инвариантные формы, минимальные модули, разложение унипотентов, орбита вектора старшего веса",
author = "Vavilov, {N. A.} and Luzgarev, {A. Yu.}",
year = "2016",
month = dec,
doi = "10.1090/spmj/1426",
language = "English",
volume = "27",
pages = "899--921",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "6",

}

RIS

TY - JOUR

T1 - NORMALIZER OF THE CHEVALLEY GROUP OF TYPE E-7

AU - Vavilov, N. A.

AU - Luzgarev, A. Yu.

PY - 2016/12

Y1 - 2016/12

N2 - The simply connected Chevalley group G(E-7, R) of type E-7 is considered in the 56-dimensional representation. The main objective is to prove that the following four groups coincide: the normalizer of the elementary Chevalley group E(E-7, R), the normalizer of the Chevalley group G(E-7, R) itself, the transporter of E(E-7, R) into G(E-7, R), and the extended Chevalley group G (E-7, R). This holds over an arbitrary commutative ring R, with all normalizers and transporters being calculated in GL(56, R). Moreover, G (E-7, R) is characterized as the stabilizer of a system of quadrics. This last result is classically known over algebraically closed fields, here it is proved that the corresponding group scheme is smooth over Z, which implies that it holds over arbitrary commutative rings. These results are a key step in a subsequent paper, devoted to overgroups of exceptional groups in minimal representations.

AB - The simply connected Chevalley group G(E-7, R) of type E-7 is considered in the 56-dimensional representation. The main objective is to prove that the following four groups coincide: the normalizer of the elementary Chevalley group E(E-7, R), the normalizer of the Chevalley group G(E-7, R) itself, the transporter of E(E-7, R) into G(E-7, R), and the extended Chevalley group G (E-7, R). This holds over an arbitrary commutative ring R, with all normalizers and transporters being calculated in GL(56, R). Moreover, G (E-7, R) is characterized as the stabilizer of a system of quadrics. This last result is classically known over algebraically closed fields, here it is proved that the corresponding group scheme is smooth over Z, which implies that it holds over arbitrary commutative rings. These results are a key step in a subsequent paper, devoted to overgroups of exceptional groups in minimal representations.

KW - Chevalley groups

KW - elementary subgroups

KW - minimal modules

KW - invariant forms

KW - decomposition of unipotents

KW - root elements

KW - highest weight orbit

KW - REPRESENTATIONS

KW - OVERGROUPS

KW - группа Шевалле

KW - элементарная подгруппа

KW - инвариантные формы

KW - минимальные модули

KW - разложение унипотентов

KW - орбита вектора старшего веса

U2 - 10.1090/spmj/1426

DO - 10.1090/spmj/1426

M3 - Article

VL - 27

SP - 899

EP - 921

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 6

ER -

ID: 7599806