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arXiv · 1907.11801

Construction of double coset system of a Coxeter group and its applications to Bruhat graphs

Masato Kobayashi
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Abstract

We develop combinatorics of parabolic double cosets in finite Coxeter groups as a follow-up of recent articles by Billey-Konvalinka-Petersen-Slofstra-Tenner and Petersen. (1) We construct a double coset system as a generalization of a two-sided analogue of a Coxeter complex and present its order structure with its local dimension function on certain connected components. As applications of double cosets to Bruhat graphs, we also prove: (2) every parabolic double coset is regular, (3) invariance of degree on Bruhat graph on lower intervals as an analogy of the one for Kazhdan-Lusztig polynomials, (4) every noncritical Bruhat interval satisfies out-Eulerian property.

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Masato Kobayashi. 2019-07-26. Construction of double coset system of a Coxeter group and its applications to Bruhat graphs. https://arxiv.org/abs/1907.11801

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