The flag variety of a complex reductive linear algebraic group G is bydefinition the quotient G/B by a Borel subgroup. It can be regarded as the setof Borel subalgebras of Lie(G). Given a nilpotent element e in Lie(G), onecalls Springer fiber the subvariety formed by the Borel subalgebras whichcontain e. Springer fibers have in general a complicated structure (notirreducible, singular). Nevertheless, a theorem by C. De Concini, G. Lusztig,and C. Procesi asserts that, when G is classical, a Springer fiber can alwaysbe paved by finitely many subvarieties isomorphic to affine spaces. In thispaper, we study varieties generalizing the Springer fibers to the context ofpartial flag varieties, that is, subvarieties of the quotient G/P by aparabolic subgroup (instead of a Borel subgroup). The main result of the paperis a generalization of De Concini, Lusztig, and Procesi's theorem to thiscontext.
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