Unitary Representations of $W$ Infinity Algebras
Satoru Odake

TL;DR
This paper investigates the structure and representations of various $W$ infinity algebras, introduces a new superalgebra extension, and classifies its representations, highlighting supersymmetry properties in different series.
Contribution
It introduces a new extended superalgebra $W_{ ext{infty}}^{M,N}$ and classifies its free field realizations into continuous and discrete series with supersymmetry analysis.
Findings
Characters of representations are computed.
A new superalgebra $W_{ ext{infty}}^{M,N}$ is constructed.
Supersymmetry exists in continuous series and under specific conditions in discrete series.
Abstract
We study the irreducible unitary highest weight representations, which are obtained from free field realizations, of infinity algebras (, , , , , ) with central charges (, , , , , ). The characters of these representations are computed. We construct a new extended superalgebra , whose bosonic sector is . Its representations obtained from a free field realization with central charge , are classified into two classes: continuous series and discrete series. For the former there exists a supersymmetry, but for the latter a supersymmetry exists only for .
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