Eigensystem and Full Character Formula of the W_{1+infinity} Algebra with c=1

TL;DR

This paper explores the representation theory of the W_{1+infinity} algebra at central charge c=1, providing explicit eigenvectors, eigenvalues, and character formulas using free field realizations.

Contribution

It introduces explicit eigenvectors and character formulas for the W_{1+infinity} algebra at c=1, advancing understanding of its structure and representations.

Findings

Eigenvectors parametrized by Young diagrams

Explicit eigenvalues for the algebra's generators

Full character formula derived

Abstract

By using the free field realizations, we analyze the representation theory of the W_{1+infinity} algebra with c=1. The eigenvectors for the Cartan subalgebra of W_{1+infinity} are parametrized by the Young diagrams, and explicitly written down by W_{1+infinity} generators. Moreover, their eigenvalues and full character formula are also obtained.