Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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GEOMETRIC REPRESENTATIONS OF FINITE GROUPS ON REAL TORIC SPACES

  • Cho, Soojin (Department of Mathematics Ajou University) ;
  • Choi, Suyoung (Department of Mathematics Ajou University) ;
  • Kaji, Shizuo (Institute of Mathematics for Industry Kyushu University)
  • Received : 2018.09.23
  • Accepted : 2018.10.30
  • Published : 2019.09.01
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Abstract

We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces $X^{\mathbb{R}}$ and simplicial complexes with characteristic matrices. We give a combinatorial description of the G-module structure of the homology of $X^{\mathbb{R}}$. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type A and B, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties.

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References

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