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Mat. Zametki, 2007, Volume 82, Issue 2, Pages 293–304 (Mi mz3792)  

This article is cited in 1 scientific paper (total in 1 paper)

On Quotient Spaces of Compact Lie Groups by Tori Centralizers

A. N. Shchetinin

N. E. Bauman Moscow State Technical University

Abstract: We consider the graph of the homogeneous space $K/L$, where $K$ is a compact Lie group and $L$ is the centralizer of a torus in $K$. We obtain a characterization of those spaces whose graphs admit embeddings in a certain standard graph. We compute the number of arcs in such graphs. We also give a simple expression for the Euler class of the homogeneous space $K/L$.

Keywords: homogeneous space, root system, simple root, graph of a root system, Euler class

DOI: https://doi.org/10.4213/mzm3792

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English version:
Mathematical Notes, 2007, 82:2, 257–266

Bibliographic databases:

UDC: 512.816
Received: 26.12.2005
Revised: 18.08.2006

Citation: A. N. Shchetinin, “On Quotient Spaces of Compact Lie Groups by Tori Centralizers”, Mat. Zametki, 82:2 (2007), 293–304; Math. Notes, 82:2 (2007), 257–266

Citation in format AMSBIB
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\paper On Quotient Spaces of Compact Lie Groups by Tori Centralizers
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\pages 257--266
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  • https://doi.org/10.4213/mzm3792
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. N. Shchetinin, “Ranks of Homotopy Groups of Homogeneous Spaces”, Math. Notes, 86:6 (2009), 850–860  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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