The maximal chains of the extended Bruhat orders on the (W x W)-orbits of an infinite Renner monoid

Details The maximal chains of the extended Bruhat orders on the (W x W)-orbits of an infinite Renner monoid The maximal chains of the extended Bruhat orders on the (W x W)-orbits of an infinite Renner monoid

2003-10-21

arxiv.org/abs/math/0310341v1

Mathematics

Combinatorics

21 pages

Scientific paper

Let (W, S) be a Coxeter system. We investigate combinatorially certain partial orders, called extended Bruhat orders, on a (W x W)-set W(N,C), which depends on W, a subset N of S, and a component C of N. We determine the length of the maximal chains between two elements. These posets generalize W equipped with its Bruhat order. They include the (W x W)-orbits of the Renner monoids of reductive algebraic monoids and of some infinite dimensional generalizations which are equipped with the partial orders obtained by the closure relations of the Bruhat and Birkhoff cells. They also include the (W x W)-orbits of certain posets obtained by generalizing the closure relation of the Bruhat cells of the wonderful compactification.

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