THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x2 = 0

For x ∈ End(K n ) satisfying x 2 = 0 let F x be the variety of full flags stable under the action of x (Springer fiber over x ). The full classification of the components of F x according to their smoothness was provided in [4] in terms of both Young tableaux and link patterns. Moreover in [2] the p...

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Veröffentlicht in:Transformation groups 2022, Vol.27 (2), p.597-633
Hauptverfasser: MANSOUR, RONIT, MELNIKOV, ANNA
Format: Artikel
Sprache:eng
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Zusammenfassung:For x ∈ End(K n ) satisfying x 2 = 0 let F x be the variety of full flags stable under the action of x (Springer fiber over x ). The full classification of the components of F x according to their smoothness was provided in [4] in terms of both Young tableaux and link patterns. Moreover in [2] the purely combinatorial algorithm to compute the singular locus of a singular component of F x is provided. However, this algorithm involves the computation of the graph of the component, and the complexity of computations grows very quickly, so that in practice it is impossible to use it. In this paper, we construct another algorithm, giving all the components of the singular locus of a singular component F σ of F x in terms of link patterns constructed straightforwardly from the link pattern of σ.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-020-09621-0