Purity of equivalued affine Springer fibers
Mark Goresky, Robert Kottwitz, Robert MacPherson
TL;DR
This paper proves that the homology of certain affine Springer fibers, associated with regular integral equivalued semisimple elements, is pure due to their paving by vector bundles over Hessenberg varieties.
Contribution
It establishes the purity of affine Springer fibers' homology by demonstrating their paving structure over Hessenberg varieties.
Findings
Homology of affine Springer fibers is pure.
Affine Springer fibers admit a paving by vector bundles over Hessenberg varieties.
Purity follows from the paving structure.
Abstract
The affine Springer fiber corresponding to a regular integral equivalued semisimple element admits a paving by vector bundles over Hessenberg varieties and hence its (Borel-Moore) homology is "pure".
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Topics in Algebra · Algebraic structures and combinatorial models