We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenberg-Virasoro algebra, having a nontrivial fi...

A family of polynomial τ -functions for the NLS-Toda hierarchy is constructed. The hierarchy is associated with the homogeneous vertex operator representation of the affine algebra g of type A (1) 1 . These τ -functions are given explicitly in terms of Schur functions that correspond to rectangular Young diagrams. It is shown that an arbitrary polynomial τ -function which is an eigenvector of d...

The Virasoro field associated to b, c ghost systems with arbitrary integer spin λ on an n-sheeted branched covering of the Riemann sphere is deformed. This leads to reducible but indecomposable representations, if the new Virasoro field acts on the space of states, enlarged by taking the tensor product over the different sheets of the surface. For λ = 1, proven LCFT structures are made explicit...

I discuss a realization of stress-tensor for parafermion theories following the generalized Frenkel-Kac construction for higher level Kac-Moody algebras. All the fields are obtained from d=rank free bosons compactified on torus. This gives an alternative realization of Virasoro algebra in terms of a non-local correction of a free field construction which does not fit the usual background charge...

We comment on the conformal boundary states of the c = 1 free boson theory on a circle which do not preserve the U(1) symmetry. We construct these Virasoro boundary states at a generic radius by a simple asymmetric shift orbifold acting on the fundamental boundary states at the self-dual radius. We further calculate the boundary entropy and find that the Virasoro boundary states at irrational r...

We derive Virasoro constraints for the zero momentum part of the QCD-like partition functions in the sector of topological charge ν. The constraints depend on the topological charge only through the combination N f + βν/2 where the value of the Dyson index β is determined by the reality type of the fermions. This duality between flavor and topology is inherited by the small-mass expansion of th...