Intersection Theory on Homogeneous Spaces of Simple Lie Group

Abstract:

Consider H^*(U_n/T_n, Z), the integral cohomology ring of homogeneous space U_n/T_n. It is a quotient ring of the polynomial ring in n variables. Particularly, the homogeneous part with degree d=dimU_n/T_n corresponds to the highest dimensional cohomology group Z, i.e., each degree d homogeneous polynomial f corresponds to an integer (chi)(f). The present article computes this correspondence explicitly. The connections with the intersection theory of the manifold U_n/T_n are also discussed. Similar result applies to the homogeneous space Sp_n/T_n.

Key words:

homogeneous space; intersection theory; intersection number

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