5 articles
Kirillov orbit method
The Kirillov orbit method, also called the orbit method, parametrizes the irreducible unitary representations of a Lie group by its coadjoint orbits; A. A. Kirillov introduced it in 1962.
Locally compact group
A locally compact group, also called a locally compact topological group, is a topological group where every point has a compact neighborhood. It is the standard setting for Haar measure and harmonic analysis.
Peter–Weyl theorem
The Peter–Weyl theorem is a 1927 result of Fritz Peter and Hermann Weyl stating that matrix coefficients of irreducible representations form an orthonormal basis of L²(G) for compact groups.
Unitary dual
The unitary dual of a group G, written Ĝ, is the set of its irreducible unitary representations, identified with the spectrum of the group C-algebra.
Unitary representation
A unitary representation is a continuous homomorphism from a topological group into the unitary operators on a Hilbert space, central to harmonic analysis and quantum mechanics.