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.
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