Roger W. Richardson proved that any parabolic subgroup of a complex semisimple Lie group admits an open dense orbit in the nilradical of its corresponding parabolic subalgebra. In the case of complex symmetric spaces we show that there exist some large classes of parabolic subgroups for which the analogous statement which fails in general, is true. Our main contribution is the extension of a th...

Let [p] = {1, . . . , p} denote a totally ordered alphabet on p letters, and let α = (α1, . . . ,αm) ∈ [p1], β = (β1, . . . ,βm) ∈ [p2]. We say that α is order-isomorphic to β if for all 1≤ i< j ≤ m one has αi < α j if and only if βi < β j. For two permutations π ∈ Sn and τ ∈ Sk, an occurrence of τ in π is a subsequence 1 ≤ i1 < i2 < .. . < ik ≤ n such that (πi1 , . . . ,πik ) is order-isomorph...

Necessary and sufficient conditions for the equivalence and congruence of matrices under the action of standard parabolic subgroups are discussed.

Necessary and sufficient conditions for the equivalence and congruence of matrices under the action of standard parabolic subgroups are discussed.

We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalizes the Munn-Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated with reductive monoids play a crucial role in our work. It turns out that the irreducible representations of certain parabolic subgroups of the Weyl groups ...

We show that the set SA(G) of equivalence classes of synchronously automatic structures on a geometrically finite hyperbolic group G is dense in the product of the sets SA(P) over all maximal parabolic subgroups P. The set BSA(G) of equivalence classes of biautomatic structures on G is isomorphic to the product of the sets BSA(P) over the cusps (conjugacy classes of maximal parabolic subgroups)...

We compute conjugacy classes in maximal parabolic subgroups of the general linear group. This computation proceeds by reducing to a “matrix problem”. Such problems involve finding normal forms for matrices under a specified set of row and column operations. We solve the relevant matrix problem in small dimensional cases. This gives us all conjugacy classes in maximal parabolic subgroups over a ...

J. Reine Angew. Math 436 (1993), pp. 209– 219. Stony Brook IMS Preprint #1991/23 December 1991 Let G ⊂ PSL(2,C) be a geometrically finite Kleinian group, with region of discontinuity Ω(G). By Ahlfors’ finiteness theorem, the quotient, Ω(G)/G, is a finite union of Riemann surfaces of finite type. Thus on it, there are only finitely many mutually disjoint free homotopy classes of simple closed cu...