Schubert functions and the number of reduced words of permutations.
Singularités génériques des variétés de Schubert covexillaires
On montre que les composantes irréductibles du lieu singulier d’une variété de Schubert dans associée à une permutation covexillaire, sont paramétrées par certains des points coessentiels du graphe de la permutation. On donne une description explicite de ces composantes et l’on décrit la singularité le long de chacune d’entre elles.
Some Investigations Concerning Kazhdan-Lusztig cells in Finite Coxeter groups of type A_n
Some new applications of orbit harmonics.
Some remarks on the algebraic structure of the finite Coxeter group .
Sortable elements for quivers with cycles.
Specht modules for Weyl groups.
Spetses.
Spherical conjugacy classes and the Bruhat decomposition
Let be a connected, reductive algebraic group over an algebraically closed field of zero or good and odd characteristic. We characterize spherical conjugacy classes in as those intersecting only Bruhat cells in corresponding to involutions in the Weyl group of .
Strong Tits alternative for subgroups of Coxeter groups.
Structure of geodesics in the Cayley graph of infinite Coxeter groups
Let (W,S) be a Coxeter system such that no two generators in S commute. Assume that the Cayley graph of (W,S) does not contain adjacent hexagons. Then for any two vertices x and y in the Cayley graph of W and any number k ≤ d = dist(x,y) there are at most two vertices z such that dist(x,z) = k and dist(z,y) = d - k. Allowing adjacent hexagons, but assuming that no three hexagons can be adjacent to each other, we show that the number of such intermediate vertices at a given distance from x and y...