In recent work ([KW1],[KW2]), Kostant and Wallach construct an action of a simply connected Lie group A ≃ C( n 2 ) on gl(n) using a completely integrable system derived from the Poisson analogue of the Gelfand-Zeitlin subalgebra of the enveloping algebra. In [KW1], the authors show that A-orbits of dimension ( n 2 ) form Lagrangian submanifolds of regular adjoint orbits in gl(n). They describe ...

ied from 1 to 500 pi. Plasma samples were obtained from EDTA-treated whole blood. Quantitation of Serum CEA by Radioimmunoassay. CEA levels in sera were determined by Todd-Egan double anti body radioimmunoassay (3) as modified by Laurence et a!. (7), using goat anti-CEA serum (Peanuts 12). CEA levels in plasma were determined either by indirect or direct Hansen Z-gel radioimmunoassay (6), as in...

A polytope is called a Coxeter polytope if its dihedral angles are integer parts of π. In this paper we prove that if a noncompact Coxeter polytope of finite volume in IH has exactly n+3 facets then n ≤ 16. We also find an example in IH and show that it is unique. 1. Consider a convex polytope P in n-dimensional hyperbolic space IH. A polytope is called a Coxeter polytope if its dihedral angles...

Billey, Konvalinka, Petersen, Solfstra, and Tenner recently presented a method for counting parabolic double cosets in Coxeter groups, used it to compute $p_n$, the number of $S_n$, $n\leq13$. In this paper, we derive new formula $p_n$ an efficient polynomial time algorithm evaluating formula. We use these results $n\leq5000$ prove asymptotic that was conjectured by Billey et al.

In this paper, given a split extension of an arbitrary Coxeter group by automorphisms of the Coxeter graph, we determine the involutions in that extension whose centralizer has finite index. Our result has applications to many problems such as the isomorphism problem of general Coxeter groups. In the argument, some properties of certain special elements and of the fixed-point subgroups by graph...

A new class of positive definite functions related to colour-length function on arbitrary Coxeter group is introduced. Extensions of positive definite functions, called the Riesz-Coxeter product, from the Riesz product on the Rademacher (Abelian Coxeter) group to arbitrary Coxeter group is obtained. Applications to harmonic analysis, operator spaces and noncommutative probability is presented. ...

A Coxeter group W is said to be rigid if, given any two Coxeter systems (W,S) and (W,S′), there is an automorphism ρ : W −→ W such that ρ(S) = S′. We consider the class of Coxeter systems (W,S) for which the Coxeter graph ΓS is complete and has only odd edge labels (such a system is said to be of “type Kn”). It is shown that if W has a type Kn system, then any other system for W is also type Kn...