On hypergeometric functions connected with quantum cohomology of flag spaces (Q1969058)

Givental's work on equivariant Gromov-Witten invariants has established the relationship between quantum cohomology and hypergeometric series [see \textit{A. B. Givental'}, Int. Math. Res. Not. 1996, No. 13, 613-663 (1996; Zbl 0881.55006)]. Consider a toral action on a compact Kähler manifold \(X\) with finitely many fixed points \(x_w\). The solutions of the differential equations arising from quantum cohomology are related to equivariant correlators \(Z_w\) associated with the \(x_w\). The correlators \(Z_w\) are the hypergeometric series associated with equivariant quantum cohomology, and can be uniquely determined by linear recursion relations. The main result in the paper under review is the explicit determination of the recursion relations for the \(Z_w\) on flag spaces \(X=G/B\). Here \(G\) is the simply connected algebraic group associated with a finite root system \(R\). Hence \(X\) is a homogeneous space for the action of the maximal torus of \(G\). The set of fixed points is in this case finite and parametrized by the Weyl group of \(R\). A simple explicit formula for the \(Z_w\) is presented in the case \(G=SL(3)\).