$W_{1+\infty }$ flows and multi-component hierarchy (KP case)

Abstract

We show that abelian subalgebras of generalized $W_{1+\infty }$ ($G{W}_{1+\infty }$) algebra gives rise to the multicomponent KP flows. The matrix elements of the related group elements in the fermionic Fock space is expressed as a product of a certain factor (generalized content product) and of a number of the Schur functions and the skew Schur functions.

References in corpus (9)

• Integrable Structure of Interface Dynamics
• Quasifinite highest weight modules over the Lie algebra of differential operators on the circle
• Generalized Kazakov-Migdal-Kontsevich Model: group theory aspects
• Schur function expansion for normal matrix model and associated discrete matrix models
• Interpolating Matrix Models for WLZZ series
• Scalar products of symmetric functions and matrix integrals
• Many-body integrable systems implied by WLZZ models
• Commutative families in DIM algebra, integrable many-body systems and $q,t$ matrix models
• Spectral curves and $W$-representations of matrix models