SUBGROUPS OF CHEVALLEY GROUPS OF TYPES B-l AND C-l CONTAINING THE GROUP OVER A SUBRING, AND CORRESPONDING CARPETS : научное издание

Описание

Тип публикации: статья из журнала

Год издания: 2020

Идентификатор DOI: 10.1090/spmj/1620

Ключевые слова: classical groups, subgroup lattice, carpet subgroups, bruhat decomposition

Аннотация: This is a continuation of the study of subgroups of the Chevalley group GP (Phi, R) over a ring R with root system Phi and weight lattice P that contain the elementary subgroup E-P (Phi, K) over a subring K of R. A. Bak and A. V. Stepanov considered recently the case of the symplectic group (simply connected group with root system Показать полностьюPhi = C-l) in characteristic 2. In the current article, that result is extended to the case of Phi = B-l and for the groups with other weight lattices. Like in the Ya. N. Nuzhin's work on the case where R is an algebraic extension of a non-perfect field K and F is not simply laced, the description involves carpet subgroups parametrized by two additive subgroups. In the second part of the article, the Bruhat decomposition is established for these carpet subgroups and it is proved that they have a split saturated Tits system. As a corollary, it is shown that they are simple as abstract groups.

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Издание

Журнал: ST PETERSBURG MATHEMATICAL JOURNAL

Выпуск журнала: Vol. 31, Is. 4

Номера страниц: 719-737

ISSN журнала: 10610022

Место издания: PROVIDENCE

Издатель: AMER MATHEMATICAL SOC

Авторы

  • Nuzhin Ya N. (Siberian Fed Univ, Inst Math & Fundamental Informat, Svobodny Prospect 79, Krasnoyarsk 660041, Russia)
  • Stepanov A.V (St Petersburg State Univ, Univ Skaya Nab 7, St Petersburg 199034, Russia)