Bruhat order and graph structures of lower intervals in Coxeter groups

Masato Kobayashi

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arxiv 1812.06266 v1 pith:RW3FKNA7 submitted 2018-12-15 math.CO

Bruhat order and graph structures of lower intervals in Coxeter groups

Masato Kobayashi This is my paper

classification math.CO

keywords bruhatlowercoxetergraphsintervalspropertyquotienttwo-sided

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We show that any lower Bruhat interval in a Coxeter group is a disjoint union of certain two-sided cosets as a consequence of Lifting Property and Subword Property. Furthermore, we describe these details in terms of Bruhat graphs, graded posets, and two-sided quotients altogether. For this purpose, we introduce some new ideas, quotient lower intervals and quotient Bruhat graphs.

Bruhat order and graph structures of lower intervals in Coxeter groups

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