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 language | English |
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Pages (from-to) | 393-418 |
Number of pages | 26 |
Journal | Selecta Mathematica, New Series |
Volume | 16 |
Issue number | 3 |
DOIs | |
State | Published - 2010 |
Keywords
- Flag varieties
- Springer fibers
- Young diagrams and tableaux
ASJC Scopus subject areas
- General Mathematics
- General Physics and Astronomy