The Satake correspondence in quantum cohomology

Appears in collection : Summer School 2011 - MODULES DE COURBES ET THEORIE DE GROMOV-WITTEN

The Satake isomorphism identi es the irreducible representations of a semisimple algebraic group with the intersection cohomologies of the Schubert varieties in the affine Grassmannian of the Langlands dual group. In the very special case where the Schubert varieties are smooth, one gets an identi cation between the so-called minuscule representations and the cohomology of the so-calledminuscule homogeneous spaces. I will explain how this extends to quantum cohomology.