Jordan algebra

Statistics

Epistemology

Operating system

Combinatorics

Physics

Unitarity

Graph

Algebra over a field

Philosophy

Algebra representation

Principal (computer security)

Political science

Vertex operator algebra

Pure mathematics

Simple (philosophy)

Conjecture

Realization (probability)

Mathematics

Computer science

Quantum mechanics

Unitary state

Vertex (graph theory)

Coset

Inventiones mathematicae

We prove the long-standing conjecture on the coset construction of the minimal series principal W-algebras of ADE types in full generality. We do this by first establishing Feigin's conjecture on the coset realization of the universal principal W-algebras, which are not necessarily simple. As consequences, the unitarity of the "discrete series" of principal W-algebras is established, a second coset realization of rational and unitary W-algebras of type A and D are given and the rationality of Kazama–Suzuki coset vertex superalgebras is derived.

W-algebras as coset vertex algebras