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arXiv · 2112.03771

Representations of Coxeter groups and homology of Coxeter graphs

Hongsheng Hu
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Abstract

We classify a class of complex representations of an arbitrary Coxeter group via characters of the integral homology of certain graphs. Such representations can be viewed as a generalization of the geometric representation and correspond to the second-highest 2-sided cell in the sense of Kazhdan-Lusztig. We also give a description of the cell representation provided by this 2-sided cell, and find out all its simple quotients for simply laced Coxeter system with no more than one circuit in the Coxeter graph.

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Hongsheng Hu. 2021-12-07. Representations of Coxeter groups and homology of Coxeter graphs. https://arxiv.org/abs/2112.03771

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