We analyze the asymptotic symmetries of near extremal Kerr black holes in four dimensions using the AdS2/CFT1 correspondence. We find a Virasoro algebra with central charge cR = 12J that is independent from the Virasoro algebra (with the same central charge) that acts on the degenerate ground state. The energy of the excitations is computed as well, and we can use Cardy’s formula to determine t...

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...

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 consider the enhancement of SL(2, R) to Virasoro algebra in a system ofN particles on AdS2. We restrict our discussion to the case of non-interacting particles, and argue that they must be treated as fermions. We find operators Ln whose commutators on the ground state, |vac〉, satisfy relations that are reminisent of c = 1 Virasoro algebra, provided N ≥ n ≥ −N . Same relations hold also on th...

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 investigate new realisations of the W 3 algebra with arbitrary central charge, making use of the fact that this algebra can be linearised by the inclusion of a spin-1 current. We use the new realisations with c = 102 and c = 100 to build non-critical and critical W 3 BRST operators. Both of these can be converted by local canonical transformations into a BRST operator for the Virasoro string...

Free field constructions for the elliptic algebra A q,p (sl 2) and Baxter's eight-vertex model Abstract Three examples of free field constructions for the vertex operators of the elliptic quantum group A q,p (sl 2) are obtained. Two of these (for p 1/2 = ±q 3/2 , p 1/2 = −q 2) are based on representation theories of the deformed Virasoro algebra, which correspond to the level 4 and level 2 Z-al...

Free field constructions for the elliptic algebra A q,p (sl 2) and Baxter's eight-vertex model Abstract Three examples of free field constructions for the vertex operators of the elliptic quantum group A q,p (sl 2) are obtained. Two of these (for p 1/2 = ±q 3/2 , p 1/2 = −q 2) are based on representation theories of the deformed Virasoro algebra, which correspond to the level 4 and level 2 Z-al...