On the singularity of the irreducible components of a Springer fiber in sln

Lucas Fresse, Anna Melnikov

Research output: Contribution to journalArticlepeer-review

Abstract

Let Bu be the Springer fiber over a nilpotent endomorphism u ∈ End(ℂn). Let J (u) be the Jordan form of u regarded as a partition of n. The irreducible components of Bu are all of the same dimension. They are labelled by Young tableaux of shape J (u). We study the question of the singularity of the components of Bu and show that all the components of Bu are nonsingular if and only if J(u) ∈ {(λ, 1, 1,...), (λ1, λ2), (λ1, λ2, 1), (2, 2, 2)}.

Original languageEnglish
Pages (from-to)393-418
Number of pages26
JournalSelecta Mathematica, New Series
Volume16
Issue number3
DOIs
StatePublished - 2010

Keywords

  • Flag varieties
  • Springer fibers
  • Young diagrams and tableaux

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy

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