Abstract We study the action of a real reductive group G on submanifold X Kähler manifold Z . suppose that compact connected Lie U with algebra $\mathfrak {u}$ extends holomorphically to an complexified $U^{\mathbb {C}}$ and -action is Hamiltonian. If $G\subset U^{\mathbb compatible, there exists gradient map $\mu _{\mathfrak p}:X \longrightarrow \mathfrak p$ where g=\mathfrak k \oplus Cartan d...

A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the Artin-Tits groups of spherical type. We generalise the well-known notion of a parabolic subgroup of an Artin-Tits group into that of a parabolic subgroup of a Garside group. We also define the more general notion...

Let G be a reductive algebraic group defined over an algebraically closed field k. Let H be a closed connected subgroup of G containing a maximal torus T of G. In [13] it was shown (at least in characteristic zero) that the parabolic subgroups of G can be characterized among all such subgroups H by a certain finiteness property of the induction functor (-)Iz and its derived functors Lk,G(-). Th...

Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I ⊆ S let gI be the corresponding semi-simple subalgebra of g. Denote by WI the Weyl group of gI and let w◦ and w I ◦ be the longest elements of W and WI , respectively. In this paper we show that the answer to Kostant’s problem, i.e. whether the universal enveloping algebra surjects on...

We define the notion of preGarside group slightly lightening the definition of Garside group so that all Artin-Tits groups are preGarside groups. This paper intends to give a first basic study on these groups. Firstly, we introduce the notion of parabolic subgroup, we prove that any preGarside group has a (partial) complemented presentation, and we characterize the parbolic subgroups in terms o...

Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic finite type groups, to FC-type We show that class is closed under intersection. also study an analog curve complex mapping group constructed by Cumplido et al. using subgroups. extend construction this complex, called subgroups...