University of Toronto's Symplectic Geometry Seminar

November 26, 2007, 2:10pm

Bahen 6183

Shizuo Kaji

Kyoto University

Chow rings of complex algebraic groups


This work should be viewed as a completion of a series of computations of Chow rings for simply-connected Lie groups by Chevalley, Grothendieck, and most recently by Marlin (1970s), who computed the Chow rings for G = Spin_n, G_2, and F_4. His method did not cover the cases of the exceptional Lie types G=E_6, E_7, and E_8. On the other hand, these Chow rings A(G) can be determined from the cohomology of the corresponding flag varieties, the latter of which were computed by Borel, Toda, Watanabe, and Nakagawa. We use the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure to obtain efficient presentations of the Chow rings of G=E_6, E_7, and E_8 via geometric generators coming from Schubert classes on G/B. This is a joint work with M.Nakagawa.