This paper shows how the Kazhdan-Lusztig theory of cells can be directly applied to establish the quasi-heredity of q-Schur algebras. The application arises because of a very strong homological property enjoyed by certain cell filtrations for q-permutation modules.

We describe all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in open circular domains. This completes the multivariate generalization of the classification program initiated by Pólya-Schur for univariate real polynomials and provides a natural framework for dealing in a uniform way with Lee-Yang type problems in statistical mechanics, com...

This presentation will introduce noncommutative analogs of monomial symmetric functions (and their dual, forgotten symmetric functions). In analogy to the classical theory, expansion of ribbon Schur functions in this basis in nonnegative. Moreover, one can define fundamental noncommutative symmetric functions by analogy with quasi-symmetric theory. The expansion of ribbon Schur functions in thi...

The quasisymmetric Macdonald polynomials G γ (X;q,t) were recently introduced by the first and second authors with Haglund, Mason, Williams in [3] to refine symmetric P λ property that (X;0,0) equals QS (X), Schur polynomial of [9]. We derive an expansion for fundamental basis functions.

4 square-root Schur RLS adaptive filter with two-fold (inputand residual) normalization is presented. The algorithm has severalattractive features suchas a fully systolic structure based on elementaryhyperbolic plane rotations. All internal variables are bounded in theunit interval and fully utilize it in successive stages due to an inherent‘‘ autoscaling ” property of t...

We present a new approach for the globalization of the primal-dual active set or equivalently the nonsmooth Newton method applied to an optimal control problem. The basic result is the equivalence of this method to a nonsmooth Newton method applied to the nonlinear Schur complement of the optimality system. Our approach does not require the construction of an additional merrit function or addit...

Schur polynomials are special cases of Schubert polynomials, which in turn dual characters flagged Weyl modules. The principal specialization and has a long history, with Macdonald famously expressing the any polynomial terms reduced words. We prove lower bound on Our result yields an alternative proof conjecture Stanley about originally proved by Weigandt.