On vertex operator realizations of Jack functions

Abstract

On the vertex operator algebra associated with rank one lattice we derive a general formula for products of vertex operators in terms of generalized homogeneous symmetric functions. As an application we realize Jack symmetric functions of rectangular shapes as well as marked rectangular shapes.

16 pages

Cited by in corpus (9)

• Plethysms, replicated Schur functions and series, with applications to vertex operators
• Applications of Laplace-Beltrami operator for Jack polynomials
• Principal subspaces for the affine Lie algebras in types $D$, $E$ and $F$
• Jack vertex operators and realization of Jack functions
• A generalization of Newton's identity and Macdonald functions
• $S$-Functions, Spectral Functions of Hyperbolic Geometry, and Vertex Operators with Applications to Structure for Weyl and Orthogonal Group Invariants
• Macdonald symmetric functions of rectangular shapes
• Deformation of Cayley's hyperdeterminants
• The h-expansion of Macdonald operators and their expression by Dunkl operators