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Half-shifted Young diagrams and homology of real Grassmannians

Authors
  • Silva, Jordan Lambert
  • Rabelo, Lonardo
Type
Preprint
Publication Date
Apr 07, 2016
Submission Date
Apr 07, 2016
Identifiers
arXiv ID: 1604.02177
Source
arXiv
License
Yellow
External links

Abstract

Let $G$ be a classical split real Lie group of type $B$, $C$, or $D$ and $P$ a maximal parabolic subgroup of $G$. The homogeneous space $G/P$ is a minimal flag manifold of $G$ and may be realized, respectively, as an even orthogonal, isotropic and odd orthogonal real Grassmannian. In this paper we compute the cellular $\mathbb{Z}$-homology group of such manifolds by a Lie theoretic approach which naturally furnish them with a cellular structure given by the Schubert varieties. The results are well understood in terms of what we call half-shifted Young diagrams whose construction is based on the the works of Buch-Kresch-Tamvakis, Ikeda-Naruse and Graham-Kreiman.

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