Witt Groups of Algebraic Groups

  • Nobuaki Yagita

    Ibaraki University, Japan


Let GkG_k be a split reductive group over a subfield kk of \bC\bC corresponding to a Lie group GG. Let TT be a maximal torus of GG. We show the isomorphism W(Gk)W(Gk/Tk)W^*(G_k)\cong W^*(G_k/T_k) of Balmer Witt groups. When kk is algebraically closed, we prove that W(Gk)W^*(G_k) is isomorphic to the topological KK-theory KO21(G/T)KO^{2*-1}(G/T) of the flag manifold G/TG/T. Then we compute it explicitly by using the fact that W(Gk)W^*(G_k) is a Hopf algebra.

Cite this article

Nobuaki Yagita, Witt Groups of Algebraic Groups. Publ. Res. Inst. Math. Sci. 50 (2014), no. 1, pp. 113–151

DOI 10.4171/PRIMS/126