Parity sheaves, moment graphs and the p -smooth locus of Schubert varieties

Peter Fiebig[1]; Geordie Williamson[2]

  • [1] Emmy-Noether-Zentrum FAY Erlangen-Nürnberg Cauerstr. 11 91058 Erlangen (Germany)
  • [2] Max-Planck-Institut für Mathematik Vivatsgasse 7 53111 Bonn (Germany)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 2, page 489-536
  • ISSN: 0373-0956

Abstract

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We show that the Braden-MacPherson algorithm computes the stalks of parity sheaves. As a consequence we deduce that the Braden-MacPherson algorithm may be used to calculate the characters of tilting modules for algebraic groups and show that the p -smooth locus of a (Kac-Moody) Schubert variety coincides with the rationally smooth locus, if the underlying Bruhat graph satisfies a GKM-condition.

How to cite

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Fiebig, Peter, and Williamson, Geordie. "Parity sheaves, moment graphs and the $p$-smooth locus of Schubert varieties." Annales de l’institut Fourier 64.2 (2014): 489-536. <http://eudml.org/doc/275566>.

@article{Fiebig2014,
abstract = {We show that the Braden-MacPherson algorithm computes the stalks of parity sheaves. As a consequence we deduce that the Braden-MacPherson algorithm may be used to calculate the characters of tilting modules for algebraic groups and show that the $p$-smooth locus of a (Kac-Moody) Schubert variety coincides with the rationally smooth locus, if the underlying Bruhat graph satisfies a GKM-condition.},
affiliation = {Emmy-Noether-Zentrum FAY Erlangen-Nürnberg Cauerstr. 11 91058 Erlangen (Germany); Max-Planck-Institut für Mathematik Vivatsgasse 7 53111 Bonn (Germany)},
author = {Fiebig, Peter, Williamson, Geordie},
journal = {Annales de l’institut Fourier},
keywords = {Modular representation theory; equivariant cohomology; moment graphs; constructible sheaves; tilting modules; Schubert varieties; $p$-smooth locus; modular representation theory; -smooth locus},
language = {eng},
number = {2},
pages = {489-536},
publisher = {Association des Annales de l’institut Fourier},
title = {Parity sheaves, moment graphs and the $p$-smooth locus of Schubert varieties},
url = {http://eudml.org/doc/275566},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Fiebig, Peter
AU - Williamson, Geordie
TI - Parity sheaves, moment graphs and the $p$-smooth locus of Schubert varieties
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 2
SP - 489
EP - 536
AB - We show that the Braden-MacPherson algorithm computes the stalks of parity sheaves. As a consequence we deduce that the Braden-MacPherson algorithm may be used to calculate the characters of tilting modules for algebraic groups and show that the $p$-smooth locus of a (Kac-Moody) Schubert variety coincides with the rationally smooth locus, if the underlying Bruhat graph satisfies a GKM-condition.
LA - eng
KW - Modular representation theory; equivariant cohomology; moment graphs; constructible sheaves; tilting modules; Schubert varieties; $p$-smooth locus; modular representation theory; -smooth locus
UR - http://eudml.org/doc/275566
ER -

References

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