Representatives for unipotent classes and nilpotent orbits

Korhonen, Mikko1; Stewart, David, I2; Thomas, Adam R.3

2021-09-01

10.1080/00927872.2021.1986519

COMMUNICATIONS IN ALGEBRA   影响因子和分区

0092-7872

1532-4125

Let G be a simple algebraic group over an algebraically closed field k of characteristic p. The classification of the conjugacy classes of unipotent elements of G(k) and nilpotent orbits of G on Lie(G) is well-established. One knows there are representatives of every unipotent class as a product of root group elements and every nilpotent orbit as a sum of root elements. We give explicit representatives in terms of a Chevalley basis for the eminent classes. A unipotent (resp. nilpotent) element is said to be eminent if it is not contained in any subsystem subgroup (resp. subalgebra), or a natural generalization if G is of type D-n. From these representatives, it is straightforward to generate representatives for any given class. Along the way we also prove recognition theorems for identifying both the unipotent classes and nilpotent orbits of exceptional algebraic groups.

Algebraic groups Lie algebras nilpotent orbits unipotent classes

SCI

英语

第一

SNSF[200021_146223] ; NSFC[11771200,11931005] ; Isaac Newton Institute for Mathematical Sciences (EPSRC)[EP/R014604/1]

Mathematics

Mathematics

WOS:000717882900001

TAYLOR & FRANCIS INC

MATHEMATICS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen, Guangdong, Peoples R China
2.Newcastle Univ, Sch Math & Stat, Newcastle Upon Tyne, Tyne & Wear, England
3.Univ Warwick, Dept Math, Coventry CV4 7AL, W Midlands, England

Korhonen, Mikko,Stewart, David, I,Thomas, Adam R.. Representatives for unipotent classes and nilpotent orbits[J]. COMMUNICATIONS IN ALGEBRA,2021.

Korhonen, Mikko,Stewart, David, I,&Thomas, Adam R..(2021).Representatives for unipotent classes and nilpotent orbits.COMMUNICATIONS IN ALGEBRA.

Korhonen, Mikko,et al."Representatives for unipotent classes and nilpotent orbits".COMMUNICATIONS IN ALGEBRA (2021).