Multiplication formulas and isomorphism theorem of ıSchur superalgebras

We introduce the notion of ?Schur superalgebra, which can be regarded as a type B/C counterpart of the q-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed q-permutation modules over Hecke algebras. Some multiplication formulas for ?Schur superalgebra are obtained to construct their canonical bases. Furthermore, we established an isomorphism theorem between the ?Scuhr superalgebras and the q-Schur superalgebras of type A, which helps us derive semisimplicity criteria of the ?Schur superalgebras.     

Asymptotic Uniqueness of Best Rational Approximants of Given Degree to Markov Functions in L 2 of the Circle

We improve over a sufficient condition given in [8] for uniqueness of a nondegenerate critical point in best rational approximation of prescribed degree over the conjugate-symmetric Hardy space of the complement of the disk. The improved condition connects to error estimates in AAK approximation, and is necessary and sufficient when the function to be approximated is of Markov type. For Markov functions whose defining measure satisfies the Szego condition, we combine what precedes with sharp asymptotics in multipoint Padé approximation from [43], [40] in order to prove uniqueness of a critical point when the degree of the approximant goes large. This lends perspective to the uniqueness issue for more general classes of functions defined through Cauchy integrals.     

Weak compactness in certain star-shift invariant subspaces

The context of much of the work in this paper is that of a backward-shift invariant subspace of the form , where B is some infinite Blaschke product. We address (but do not fully answer) the question: For which B can one find a (convergent) sequence in K_B such that the sequence of real measures converges weak-star to some nontrivial singular measure on ? We show that, in order for this to hold, K_B must contain functions with nontrivial singular inner factors. And in a rather special setting, we show that this is also sufficient. Much of the paper is devoted to finding conditions (on B) that guarantee that K_B has no functions with nontrivial singular inner factors. Our primary result in this direction is based on the “geometry” of the zero set of B.     

Relative equidimensionality and stability of actions¶of a reductive algebraic group

In order to inquire into invariants of non-semisimple groups, we introduce and study relative versions of equidimensionality and stabilty, which are called relative quasi-equidimensionality and relative stability, of actions of affine algebraic groups, especially of reductive groups, on affine varieties. As an application of our results, for complex reductive groups of semisimple rank one, we characterize, respectively, relatively stable representations and relatively equidimensional representations and, consequently, show that every equidimensional representation is cofree. Received: 23 October 1998     

The algebraic torus theorem

A structure theorem is proved for a finitely generated group with a finitely generated virtually polycyclic codimension one subgroup. Oblatum 12-II-1999 & 18-XI-1999?Published online: 21 February 2000     

Commutant lifting and interpolation: The time-varying case

We show how the commutant lifting theorem for nest algebras due to Paulsen and Power can be used to give a unified framework for the treatment of a variety of interpolation problems for nest algebras which have been considered recently in the literature. Applications include the treatment of robust control for time-varying systems.Partially supported by NSF grant DMS-9500912     

Flocks and ovals

An infinite family of q-clans, called the Subiaco q-clans, is constructed for q=2^e. Associated with these q-clans are flocks of quadratic cones, elation generalized quadrangles of order (q ², q), ovals of PG(2, q) and translation planes of order q ² with kernel GF(q). It is also shown that a q-clan, for q=2^e, is equivalent to a certain configuration of q+1 ovals of PG(2, q), called a herd.W. Cherowitzo gratefully acknowledges the support of the Australian Research Council and has the deepest gratitude and warmest regards for the Combinatorial Computing Research Group at the University of Western Australia for their congenial hospitality and moral support. I. Pinneri gratefully acknowledges the support of a University of Western Australia Research Scholarship.