Coxeter groups, Coxeter monoids and the Bruhat order
نویسندگان
چکیده
منابع مشابه
The Order Dimension of Bruhat Order on Infinite Coxeter Groups
We give a quadratic lower bound and a cubic upper bound on the order dimension of the Bruhat (or strong) ordering of the affine Coxeter group Ãn. We also demonstrate that the order dimension of the Bruhat order is infinite for a large class of Coxeter groups.
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§1 THE PROOF OF THEOREM 1. Fix a Coxeter group (W,S). The terminolog “ an expression of W ”means an element of W being written as a product of elements of S. We say an expression w of W is reduced if w is a product of `(w) elements of S. Given two expressions s1s2 · · · sk and t1t2 · · · tm of W with si, tj ∈ S, we write s1s2 · · · sk ≡ t1t2 · · · tm if otherwise. We say that two expressions g ...
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If G is a split reductive group and B a Borel subgroup then G is the disjoint union of the BwB as w ranges over the Weyl group of a maximal torus in B. The closure of BwB is the union of certain double cosets BxB, where the x that occur can be characterized in purely combinatorial terms. Somewhat surprisingly, this combinatorial definition may be extended to define the Bruhat closure operation ...
متن کاملPartial symmetry, reflection monoids and Coxeter groups
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders.
متن کاملEssays on Coxeter groups Coxeter elements in finite Coxeter groups
A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2013
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-013-0464-7