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http://dx.doi.org/10.4134/JKMS.j180646

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)
Publication Information
Journal of the Korean Mathematical Society / v.56, no.5, 2019 , pp. 1265-1283 More about this Journal
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.
Keywords
real toric variety; Weyl group; representation; poset topology; Specht module; building set; nestohedron;
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