Orbit method: Difference between revisions

Revision as of 13:36, 21 June 2021

Revision as of 21:26, 5 February 2022

Line 1:

{{Short description|constructionConstruction in representation theory}}

{{Use dmy dates|date=September 2015}}

In [[mathematics]], the '''orbit method''' (also known as the '''Kirillov theory''', '''the method of coadjoint orbits''' and by a few similar names) establishes a correspondence between irreducible [[unitary representation]]s of a [[Lie group]] and its [[coadjoint orbit]]s: orbits of the [[Group action (mathematics)|action of the group]] on the dual space of its [[Lie algebra]]. The theory was introduced by {{harvs|txt|last=Kirillov|authorlink=Alexandre Kirillov|year1=1961|year2=1962}} for [[nilpotent group]]s and later extended by [[Bertram Kostant]], [[Louis Auslander]], [[Lajos Pukánszky]] and others to the case of [[solvable group]]s. [[Roger Evans Howe|Roger Howe]] found a version of the orbit method that applies to ''p''-adic Lie groups.<ref>{{Citation | last=Howe | first=Roger | title=Kirillov theory for compact p-adic groups | year=1977 | journal=[[Pacific Journal of Mathematics]] | volume=73 | issue=2 | pages=365–381 | doi=10.2140/pjm.1977.73.365 | doi-access=free }}</ref>