## Osaka Journal of Mathematics

### Weyl group symmetry on the GKM graph of a GKM manifold with an extended Lie group action

Shizuo Kaji

#### Abstract

We consider the class of manifolds with compact Lie group actions which restrict to GKM-actions on the maximal torus. First, we see their GKM-graphs admit symmetry of the Weyl groups. And then, we study its combinatorial abstraction; starting with abstract GKM-graphs with symmetry, we derive certain properties which reflect topology in a purely combinatorial way.

#### Article information

Source
Osaka J. Math., Volume 52, Number 1 (2015), 31-43.

Dates
First available in Project Euclid: 24 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1427202870

Mathematical Reviews number (MathSciNet)
MR3326600

Zentralblatt MATH identifier
1316.55003

#### Citation

Kaji, Shizuo. Weyl group symmetry on the GKM graph of a GKM manifold with an extended Lie group action. Osaka J. Math. 52 (2015), no. 1, 31--43. https://projecteuclid.org/euclid.ojm/1427202870

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