Pairs of microweights tori in GL_n

Standard

Pairs of microweights tori in GL_n. / Nesterov, Vladimir Viktorovich ; Vavilov, Nikolay Alexandrovich.

в: Chebyshevskii Sbornik, Том 21, № 4, 2020, стр. 152-161.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{4c07e23666a44a60841d81469baf4b4e,

title = "Pairs of microweights tori in GL_n",

abstract = "In the present note we prove a reduction theorem for subgroups of the general linear group GL(n, ) over a skew-field , generated by a pair of microweight tori of the same type. It turns out, that any pair of tori of residue m is conjugate to such a pair in GL(3m, ), and the pairs that cannot be further reduced to GL(3m − 1, ) form a single GL(3m, )-orbit. For the case m = 1 this leaves us with the analysis of GL(2, ), that was carried through some two decades ago by the second author, Cohen, Cuypers and Sterk. For the next case m = 2 this means that the only cases to be considered are GL(4, ) and GL(5, ). In these cases the problem can be fully resolved by (direct but rather lengthy) matrix calculations, which are relegated to a forthcoming paper by the authors.",

keywords = "Diagonal subgroup, General linear group, Mtori, Semisimple root subgroups, Unipotent root subgroups",

author = "Nesterov, {Vladimir Viktorovich} and Vavilov, {Nikolay Alexandrovich}",

year = "2020",

doi = "10.22405/2226-8383-2020-21-4-152-161",

language = "English",

volume = "21",

pages = "152--161",

journal = "Chebyshevskii Sbornik",

issn = "2226-8383",

publisher = "Тульский государственный педагогический университет им. Л. Н. Толстого",

number = "4",

}

RIS

TY - JOUR

T1 - Pairs of microweights tori in GL_n

AU - Nesterov, Vladimir Viktorovich

AU - Vavilov, Nikolay Alexandrovich

PY - 2020

Y1 - 2020

N2 - In the present note we prove a reduction theorem for subgroups of the general linear group GL(n, ) over a skew-field , generated by a pair of microweight tori of the same type. It turns out, that any pair of tori of residue m is conjugate to such a pair in GL(3m, ), and the pairs that cannot be further reduced to GL(3m − 1, ) form a single GL(3m, )-orbit. For the case m = 1 this leaves us with the analysis of GL(2, ), that was carried through some two decades ago by the second author, Cohen, Cuypers and Sterk. For the next case m = 2 this means that the only cases to be considered are GL(4, ) and GL(5, ). In these cases the problem can be fully resolved by (direct but rather lengthy) matrix calculations, which are relegated to a forthcoming paper by the authors.

AB - In the present note we prove a reduction theorem for subgroups of the general linear group GL(n, ) over a skew-field , generated by a pair of microweight tori of the same type. It turns out, that any pair of tori of residue m is conjugate to such a pair in GL(3m, ), and the pairs that cannot be further reduced to GL(3m − 1, ) form a single GL(3m, )-orbit. For the case m = 1 this leaves us with the analysis of GL(2, ), that was carried through some two decades ago by the second author, Cohen, Cuypers and Sterk. For the next case m = 2 this means that the only cases to be considered are GL(4, ) and GL(5, ). In these cases the problem can be fully resolved by (direct but rather lengthy) matrix calculations, which are relegated to a forthcoming paper by the authors.

KW - Diagonal subgroup

KW - General linear group

KW - Mtori

KW - Semisimple root subgroups

KW - Unipotent root subgroups

UR - http://www.scopus.com/inward/record.url?scp=85101457738&partnerID=8YFLogxK

U2 - 10.22405/2226-8383-2020-21-4-152-161

DO - 10.22405/2226-8383-2020-21-4-152-161

M3 - Article

AN - SCOPUS:85101457738

VL - 21

SP - 152

EP - 161

JO - Chebyshevskii Sbornik

JF - Chebyshevskii Sbornik

SN - 2226-8383

IS - 4

ER -

ID: 76612189

Standard

Harvard

APA

Vancouver

Author

BibTeX

RIS