Singular components of Springer fibers in the two-column case

Lucas Fresse[1]

  • [1] Weizmann Institute of Science Department of Mathematics Rehovot 76100 (Israel)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 6, page 2429-2444
  • ISSN: 0373-0956

Abstract

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We consider the Springer fiber ℬ u corresponding to a nilpotent endomorphism u of nilpotent order 2 . As a first result, we give a description of the elements of a given component of ℬ u which are fixed by the action of the standard torus relative to some Jordan basis of u . By using this result, we establish a necessary and sufficient condition of singularity for the components of ℬ u .

How to cite

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Fresse, Lucas. "Singular components of Springer fibers in the two-column case." Annales de l’institut Fourier 59.6 (2009): 2429-2444. <http://eudml.org/doc/10459>.

@article{Fresse2009,
abstract = {We consider the Springer fiber $\mathcal\{B\}_u$ corresponding to a nilpotent endomorphism $u$ of nilpotent order $2$. As a first result, we give a description of the elements of a given component of $\mathcal\{B\}_u$ which are fixed by the action of the standard torus relative to some Jordan basis of $u$. By using this result, we establish a necessary and sufficient condition of singularity for the components of $\mathcal\{B\}_u$.},
affiliation = {Weizmann Institute of Science Department of Mathematics Rehovot 76100 (Israel)},
author = {Fresse, Lucas},
journal = {Annales de l’institut Fourier},
keywords = {Flag varieties; Springer fibers; singularity criteria; Young tableaux; flag varieties},
language = {eng},
number = {6},
pages = {2429-2444},
publisher = {Association des Annales de l’institut Fourier},
title = {Singular components of Springer fibers in the two-column case},
url = {http://eudml.org/doc/10459},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Fresse, Lucas
TI - Singular components of Springer fibers in the two-column case
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 6
SP - 2429
EP - 2444
AB - We consider the Springer fiber $\mathcal{B}_u$ corresponding to a nilpotent endomorphism $u$ of nilpotent order $2$. As a first result, we give a description of the elements of a given component of $\mathcal{B}_u$ which are fixed by the action of the standard torus relative to some Jordan basis of $u$. By using this result, we establish a necessary and sufficient condition of singularity for the components of $\mathcal{B}_u$.
LA - eng
KW - Flag varieties; Springer fibers; singularity criteria; Young tableaux; flag varieties
UR - http://eudml.org/doc/10459
ER -

References

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  1. F. Y. C Fung, On the topology of components of some Springer fibers and their relation to Kazhdan-Lusztig theory, Adv. Math. (2003), 244-276 Zbl1035.20004MR1994220
  2. A. Melnikov, Description of B -orbit closures of order 2 in upper triangular matrices, Transf. Groups (2006), 217-247 Zbl1196.14040MR2231186
  3. A. Melnikov, N. G. J. Pagnon, Reducibility of the intersections of components of a Springer fiber Zbl1172.14033
  4. P. Slodowy, Four lectures on simple groups and singularities, Communications of the Mathematical Institute 11 (1980), Rijksuniversiteit Utrecht Zbl0425.22020MR563725
  5. N. Spaltenstein, Classes unipotentes et sous-groupes de Borel, Lecture Notes in Mathematics 946 (1982), Springer-Verlag, Berlin-New York Zbl0486.20025MR672610
  6. J. A. Vargas, Fixed points under the action of unipotent elements of S L ( n ) in the flag variety, Bol. Soc. Mat. Mexicana (1979), 1-14 Zbl0458.14019MR579665

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