Work

Classification of coadjoint orbits for the maximal unipotent subgroup in the simple group of type F_4

Year: 2025

Type: article

Abstract: Let N be the maximal unipotent subgroup in the simple algebraic group of type Φ. It naturally acts on the space dual to the Lie algebra n of N, and this action is called coadjoint. Such orbits play the key role in the orbit method of A.A. Kirillov. In this work, we classify the orbits of this action in the case of Φ = F_4 in terms of supports of canonical forms. This means that we will present a set S of linear forms such that for any coadjoint orbit there exists a unique form from S belonging to that orbit. The set of canonical forms will be explicitly described in terms of supports.

Source: Communications in Mathematics

DOI: 10.46298/cm.16015

Author: Matvey A. Surkov

Institution: Samara National Research University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Ministry of Science and Higher Education of the Russian Federation

Awards: G2258008615, G597338630, G6444257319