Suho Oh ; Hwanchul Yoo - Bruhat order, rationally smooth Schubert varieties, and hyperplane arrangements

dmtcs:2835 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2835
Bruhat order, rationally smooth Schubert varieties, and hyperplane arrangementsArticle

Authors: Suho Oh 1; Hwanchul Yoo 1

  • 1 Department of Mathematics [MIT]

We link Schubert varieties in the generalized flag manifolds with hyperplane arrangements. For an element of a Weyl group, we construct a certain graphical hyperplane arrangement. We show that the generating function for regions of this arrangement coincides with the Poincaré polynomial of the corresponding Schubert variety if and only if the Schubert variety is rationally smooth.

https://doi.org/10.46298/dmtcs.2835
Source: HAL:hal-01186263v1
Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Bruhat order,Schubert Variety,Rational Smoothness,Palidromic,Hyperplanes,Coxeter arrangement,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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