We deal with solitons of the mean curvature flow. The definition \textit{translating on a light-like direction} in Minkowski 3-space is introduced. Firstly, we classify those which are graphical, \textit{translation surfaces}, obtaining space-like and time-like, entire not entire, complete incomplete examples. Among them, all our time-like examples incomplete. second family consists invariant b...

Let (G, K) be one of the following classical irreducible Hermitian symmetric pairs of noncompact type: (SU(p, q), S (U(p) × U(q))), (Sp(n,R),U(n)), or (SO(2n),U(n)). Let GC and KC be complexifications of G and K, respectively, and let P be a maximal parabolic subgroup of GC whose Levi subgroup is KC. Let V be the holomorphic part of the complexifiaction of the tangent space at the origin of G/K...

We enlarge a Coxeter group into category, with one object for each finite parabolic subgroup, encoding the combinatorics of double cosets. This singular monoid, is connected to geometry partial flag varieties. Our main result presentation this category by generators and relations. also provide new description reduced expressions describe all braid relations between such expressions, prove an an...

Abstract Let $$\mathcal {G}$$ G be a connected reductive group over $$\mathbf {Q}$$ Q such that $$G = \mathcal {G}/\mathbf {Q}_p$$ = / p is quasi-split, and let $$Q \subset G$$ ? ...

We continue the study of the one-dimensional E10 coset model (massless spinning particle motion on E10/K(E10)) whose dynamics at low levels is known to coincide with the equations of motion of maximal supergravity theories in appropriate truncations. We show that the coset dynamics (truncated at levels l ≤ 3) can be consistently restricted by requiring the vanishing of a set of constraints whic...

Let (AS , S) be an Artin-Tits and X a subset of S ; denote by AX the subgroup of AS generated by X. When AS is of spherical type, we prove that the normalizer and the commensurator of AX in AS are equal and are the product of AX by the quasi-centralizer of AX in AS . Looking to the associated monoids A + S and A + X , we describe the quasi-centralizer of A+X in A + S thanks to results in Coxete...

Introduction. The problem of classifying the tempered spectrum of a connected reductive quasi-split group, defined over a local field, F, of characteristic zero, consists of three parts. The first is to classify the discrete series representations of any Levi subgroup. The second step is to understand the rank one Plancherel measures, which is equivalent to understanding the reducibility of tho...

We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, and whose intersection is a separable subgroup, there are finite index subgrou...

Let H be a subgroup of a finite group G. We use Markov chains to quantify how large r should be so that the decomposition of the r tensor power of the representation of G on cosets on H behaves (after renormalization) like the regular representation of G. For the case where G is a symmetric group and H a parabolic subgroup, we find that this question is precisely equivalent to the question of h...