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We consider the derived category of coherent sheaves on a complex vectorspace equivariant with respect to an action of a finite reflection group G. Insome cases, including Weyl groups of type A, B, G_2, F_4, as well as the groupsG(m,1,n), we construct a semiorthogonal decomposition of this category, indexedby the conjugacy classes of G. The pieces of this decompositions are equivalentto the derived categories of coherent sheaves on the quotient-spaces V^g/C(g),where C(g) is the centralizer subgroup of g in G. In the case of the Weylgroups the construction uses some key results about the Springercorrespondence, due to Lusztig, along with some formality statementgeneralizing a result of Deligne. We also construct global analogs of some ofthese semiorthogonal decompositions involving derived categories of equivariantcoherent sheaves on C^n, where C is a smooth curve.

Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups