Results 21 to 30 of about 833 (53)
Garside families in Artin-Tits monoids and low elements in Coxeter groups [PDF]
, 2014 We show that every finitely generated Artin-Tits group admits a finite Garside family, by introducing the notion of a low element in a Coxeter group and proving that the family of all low elements in a Coxeter system (W, S) with S finite includes S and ...
Dehornoy, Patrick +2 more
core +3 more sources
Bender–Knuth Billiards in Coxeter Groups
Forum of Mathematics, SigmaLet $(W,S)$ be a Coxeter system, and write $S=\{s_i:i\in I\}$ , where I is a finite index set. Fix a nonempty convex subset $\mathscr {L}$ of W. If W is of type A, then $\mathscr {L}$ is the set of linear extensions of a poset,
Grant Barkley +4 more
doaj +1 more source
Orthogonal roots, Macdonald representations, and quasiparabolic sets
Forum of Mathematics, SigmaLet W be a simply laced Weyl group of finite type and rank n. If W has type $E_7$ , $E_8$ or $D_n$ for n even, then the root system of W has subsystems of type $nA_1$ .
R. M. Green, Tianyuan Xu
doaj +1 more source
Linear syzygies, flag complexes, and regularity
, 2014 We show that for every positive integer R there exist monomial ideals generated in degree two, with linear syzygies, and regularity of the quotient equal to R. Such examples can not be found among Gorenstein ideals since the regularity of their quotients
Constantinescu, Alexandru +2 more
core +1 more source
A canonical system of basic invariants of a finite reflection group
, 2014 A canonical system of basic invariants is a system of invariants satisfying a set of differential equations. The properties of a canonical system are related to the mean value property for polytopes.
Nakashima, Norihiro, Tsujie, Shuhei
core +1 more source
Affine Bruhat order and Demazure products
Forum of Mathematics, SigmaWe give new descriptions of the Bruhat order and Demazure products of affine Weyl groups in terms of the weight function of the quantum Bruhat graph.
Felix Schremmer
doaj +1 more source
Basic differential forms for actions of Lie groups
, 1994 A section of a Riemannian $G$-manifold $M$ is a closed submanifold $\Sigma$ which meets each orbit orthogonally. It is shown that the algebra of $G$-invariant differential forms on $M$ which are horizontal in the sense that they kill every vector which ...
Michor, Peter W.
core +6 more sources
Commensurators of parabolic subgroups of Coxeter groups
, 1996 Let $(W,S)$ be a Coxeter system, and let $X$ be a subset of $S$. The subgroup of $W$ generated by $X$ is denoted by $W_X$ and is called a parabolic subgroup. We give the precise definition of the commensurator of a subgroup in a group. In particular, the
Paris, Luis
core +2 more sources
The flat closing problem for buildings
, 2014 Using the notion of a strongly regular hyperbolic automorphism of a locally finite Euclidean building, we prove that any (not necessarily discrete) closed, co-compact subgroup of the type-preserving automorphisms group of a locally finite general non ...
Ciobotaru, Corina
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Real Root Conjecture fails for five and higher dimensional spheres
, 2005 A construction of convex flag triangulations of five and higher dimensional spheres, whose h-polynomials fail to have only real roots, is given. We show that there is no such example in dimensions lower than five. A condition weaker than realrootedness
Gal, Swiatoslaw R.
core +1 more source