Results 11 to 20 of about 756 (27)

Orthogonal roots, Macdonald representations, and quasiparabolic sets

Forum of Mathematics, Sigma
Let 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, Kahle, Thomas, Varbaro, Matteo   +2 more
core   +1 more source

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

Affine Bruhat order and Demazure products

Forum of Mathematics, Sigma
We 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

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
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

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

On Normal Subgroups of Coxeter Groups Generated by Standard Parabolic Subgroups

, 2005
We discuss one construction of nonstandard subgroups in the category of Coxeter groups. Two formulae for the growth series of such a subgroups are given.
M. R. Bridson, M. W. Davis, M. W. Davis, N. Bourbaki, Światosław R. Gal   +4 more
core   +1 more source

Crystallographic arrangements: Weyl groupoids and simplicial arrangements

, 2010
We introduce the simple notion of a "crystallographic arrangement" and prove a one-to-one correspondence between these arrangements and the connected simply connected Cartan schemes for which the real roots are a finite root system (up to equivalence on ...
Cuntz, Michael
core   +1 more source

On Lusztig's map for spherical unipotent conjugacy classes

, 2013
We provide an alternative description of the restriction to spherical unipotent conjugacy classes, of Lusztig's map Psi from the set of unipotent conjugacy classes in a connected reductive algebraic group to the set of conjugacy classes of its Weyl group.
Carnovale, Giovanna, Costantini, Mauro
core   +1 more source