Abstract:
Simple singularities are classified by Dynkin diagrams of type ADE.
Let $\mathfrak g$ be the corresponding finite-dimensional Lie algebra,
and $W$ its Weyl group. The set of $\mathfrak g$-invariants in the
basic representation of the affine Kac–Moody algebra $\hat{\mathfrak
g}$ is known as a $\mathcal W$-algebra and is a subalgebra of the
Heisenberg vertex algebra $\mathcal F$. Using period integrals, we
construct an analytic continuation of the twisted representation of
$\mathcal F$. Our construction yields a global object, which may be
called a $W$-twisted representation of $\mathcal F$. Our main result
is that the total descendant potential of the singularity, introduced
by Givental, is a highest weight vector for the $\mathcal W$-algebra.
(Joint work with T. Milanov.)
