On tangent cones to Schubert varieties in type E

Mikhail V. Ignatyev; Aleksandr A. Shevchenko

Communications in Mathematics (2020)

  • Volume: 28, Issue: 2, page 179-197
  • ISSN: 1804-1388

Abstract

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We consider tangent cones to Schubert subvarieties of the flag variety G / B , where B is a Borel subgroup of a reductive complex algebraic group G of type E 6 , E 7 or E 8 . We prove that if w 1 and w 2 form a good pair of involutions in the Weyl group W of G then the tangent cones C w 1 and C w 2 to the corresponding Schubert subvarieties of G / B do not coincide as subschemes of the tangent space to G / B at the neutral point.

How to cite

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Ignatyev, Mikhail V., and Shevchenko, Aleksandr A.. "On tangent cones to Schubert varieties in type $E$." Communications in Mathematics 28.2 (2020): 179-197. <http://eudml.org/doc/297247>.

@article{Ignatyev2020,
abstract = {We consider tangent cones to Schubert subvarieties of the flag variety $G/B$, where $B$ is a Borel subgroup of a reductive complex algebraic group $G$ of type $E_6$, $E_7$ or $E_8$. We prove that if $w_1$ and $w_2$ form a good pair of involutions in the Weyl group $W$ of $G$ then the tangent cones $C_\{w_1\}$ and $C_\{w_2\}$ to the corresponding Schubert subvarieties of $G/B$ do not coincide as subschemes of the tangent space to $G/B$ at the neutral point.},
author = {Ignatyev, Mikhail V., Shevchenko, Aleksandr A.},
journal = {Communications in Mathematics},
keywords = {flag variety; Schubert variety; tangent cone; involution in the Weyl group; Kostant-Kumar polynomial},
language = {eng},
number = {2},
pages = {179-197},
publisher = {University of Ostrava},
title = {On tangent cones to Schubert varieties in type $E$},
url = {http://eudml.org/doc/297247},
volume = {28},
year = {2020},
}

TY - JOUR
AU - Ignatyev, Mikhail V.
AU - Shevchenko, Aleksandr A.
TI - On tangent cones to Schubert varieties in type $E$
JO - Communications in Mathematics
PY - 2020
PB - University of Ostrava
VL - 28
IS - 2
SP - 179
EP - 197
AB - We consider tangent cones to Schubert subvarieties of the flag variety $G/B$, where $B$ is a Borel subgroup of a reductive complex algebraic group $G$ of type $E_6$, $E_7$ or $E_8$. We prove that if $w_1$ and $w_2$ form a good pair of involutions in the Weyl group $W$ of $G$ then the tangent cones $C_{w_1}$ and $C_{w_2}$ to the corresponding Schubert subvarieties of $G/B$ do not coincide as subschemes of the tangent space to $G/B$ at the neutral point.
LA - eng
KW - flag variety; Schubert variety; tangent cone; involution in the Weyl group; Kostant-Kumar polynomial
UR - http://eudml.org/doc/297247
ER -

References

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