Exact modular S-transforms are derived for GGEs in the symplectic fermion theory, agreeing with conjectures for the W3 zero mode and mirroring free-fermion results for the KdV subset.
Eigensystem and Full Character Formula of the W_{1+infinity} Algebra with c=1
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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.
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Modular Properties of Symplectic Fermion Generalised Gibbs Ensemble
Exact modular S-transforms are derived for GGEs in the symplectic fermion theory, agreeing with conjectures for the W3 zero mode and mirroring free-fermion results for the KdV subset.