In this paper, we analyze Virasoro conformal blocks in the limit when operator exchange dimension is taking to be large comparison with other parameters dependence of block. We do by using Zamolodchikov's recursion relations. found a dramatically simplified solution at leading order an inverse power expansion terms quasi-modular form Eisenstein series representation. compare existing results ob...

Relation between the Virasoro constraints and KP integrability (determinant formulas) for matrix models is a lasting mystery. We elaborate on claim that situation improved when enhanced to super-integrability, i.e. explicit formulas Gaussian averages of characters. In this case, are equivalent simple recursive formulas, which have appropriate combinations characters as their solutions. Moreover...

A weight two vector v of a vertex operator algebra is called a conformal vector with central charge c if the component operators Lv(n) for n ∈ Z of Y (v, z) = ∑ n∈Z Lv(n)z −n−2 satisfy the Virasoro algebra relation with central charge c. In this case, the vertex operator subalgebra Vir(v) generated by v is isomorphic to a Virasoro vertex operator algebra with central charge c ([FZ], [M]). Let V...

In this article, certain indecomposable Virasoro modules are studied. Specifically, the Virasoro mode L0 is assumed to be non-diagonalisable, possessing Jordan blocks of rank two. Moreover, the module is further assumed to have a highest weight submodule, the “left module”, and that the quotient by this submodule yields another highest weight module, the “right module”. Such modules, which have...

In this paper, we prove formulas for the action of Virasoro operators on Hall–Littlewood polynomials at roots unity.

We show that the Virasoro conjecture in Gromov–Witten theory holds for the the total space of a toric bundle E → B if and only if it holds for the base B. The main steps are: (i) we establish a localization formula that expresses Gromov–Witten invariants of E, equivariant with respect to the fiberwise torus action, in terms of genus-zero invariants of the toric fiber and all-genus invariants of...