Transformation Groups c©Birkhäuser Boston (2008) EQUIVARIANT CHOW RING AND CHERN CLASSES OF WONDERFUL SYMMETRIC VARIETIES OF MINIMAL RANK

Dedicated to Bert Kostant on the occasion of his 80th birthday Abstract. We describe the equivariant Chow ring of the wonderful compactification X of a symmetric space of minimal rank, via restriction to the associated toric variety Y. Also, we show that the restrictions to Y of the tangent bundle TX and its logarithmic analogue SX decompose into a direct sum of line bundles. This yields closed formulas for the equivariant Chern classes of TX and SX, and, in turn, for the Chern classes of reductive groups considered by Kiritchenko. The purpose of this paper is to describe the equivariant intersection ring and equivariant Chern classes of a class of almost homogeneous varieties, namely, won-derful symmetric varieties of minimal rank; these include the wonderful compact-ifications of semisimple groups of adjoint type