 Abstract : A simplicial complex $K$ with vertex labelling. in an $mathbb{F}_2$ vector space gives rise to a real toric space. When a finite group $G$ acts on $K$ satisfying a certain condition, it induces an action on the toric space. We investigate the case when $(K, lambda)$ is associated to a root system, and $G$ is its Weyl group. In particular, we give a concrete description of the Weyl group representation on the cohomology of the associated real toric space for type-A root systems. This is joint work with Soojin Cho and Suyoung Choi. |
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