TY - JOUR

T1 - Subgroups of chevalley groups of types Bl and Cl containing the group over a subring, and corresponding carpets

AU - Nuzhin, Ya N.

AU - Stepanov, A. V.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - Abstract. This is a continuation of the study of subgroups of the Chevalley group GP (Φ, R) over a ring R with root system Φ and weight lattice P that contain the elementary subgroup EP (Φ, 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 Φ = Cl) in characteristic 2. In the current article, that result is extended to the case of Φ = Bl 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 nonperfect field K and Φ 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.

AB - Abstract. This is a continuation of the study of subgroups of the Chevalley group GP (Φ, R) over a ring R with root system Φ and weight lattice P that contain the elementary subgroup EP (Φ, 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 Φ = Cl) in characteristic 2. In the current article, that result is extended to the case of Φ = Bl 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 nonperfect field K and Φ 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.

KW - Bruhat decomposition

KW - Carpet subgroups

KW - Classical groups

KW - Subgroup lattice

UR - http://www.scopus.com/inward/record.url?scp=85087629846&partnerID=8YFLogxK

U2 - 10.1090/SPMJ/1620

DO - 10.1090/SPMJ/1620

M3 - Article

AN - SCOPUS:85087629846

VL - 31

SP - 719

EP - 737

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 4

ER -