Purity of Equivalued Affine Springer Fibers Mark Goresky, Robert Kottwitz, and Robert Macpherson
نویسندگان
چکیده
Let k be an algebraically closed field, G a connected reductive group over k, and A a maximal torus in G. We write g for the Lie algebra of G and a for X∗(A)⊗ZR. Let F = k((ǫ)) be the field of formal Laurent series over k and let o = k[[ǫ]] be the subring of formal power series. We fix an algebraic closure F̄ of F . We write G and g for G(F ) and g(F ) := g ⊗k F respectively. Let y ∈ a and write Gy and gy for the associated (connected) parahoric subgroup and subalgebra respectively. For example, if y = 0, then Gy = G(o) and gy = g(o), while if y lies in the interior of an alcove, then Gy (resp., gy) is an Iwahori subgroup (resp. subalgebra). We write Fy for the k-ind-scheme G/Gy. When y = 0 for example, Fy is the affine Grassmannian G(F )/G(o). Any u ∈ g determines a closed subset
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Purity of Equivalued Affine Springer Fibers
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