Irreducible decompositions of Fock representations of the Virasoro algebra

DOI10.1007/BF00402251zbMath0529.17009MaRDI QIDQ787256

Minoru Wakimoto, Hiro-Fumi Yamada

Publication date: 1983

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Young diagramFock representationVirasoro algebraHirota bilinear equationcharacter polynomialmodified Kadomtsev-Petviashvili hierarchy

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Infinite-dimensional Lie (super)algebras (17B65) Applications of Lie groups to the sciences; explicit representations (22E70) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Constructive quantum field theory (81T08) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Graded Lie (super)algebras (17B70)

Related Items

Coset algebras, integrable hierarchies and matrix models, Lie algebraic approach to \(\tau\)-functions and its equations, On the uniqueness of the twisted representation in the \(\mathbb{Z}_2\) orbifold construction of a conformal field theory from a lattice, The operator algebra of orbifold models, On vertex operator realizations of Jack functions, Fock space resolutions of the Virasoro highest weight modules with \(c\leqslant 1\), A novel realization of the Virasoro algebra in number state space, Singular vectors for the WN algebras, BRST analysis of physical states for 2D gravity coupled to \(c\leqq{}1\) matter, Superconformal field theory and Jack superpolynomials, The basic representation of the extended affine Lie algebra of type \(A_ 1^{(1)}\) and the BKP hierarchy

Cites Work

• Solitons and infinite dimensional Lie algebras
• Unitary representations of some infinite dimensional groups
• Invariant skew-symmetric differential operators on the line and Verma modules over the Virasoro algebra