We present two new algorithms for computing all Schur functions sκ(x1, . . . ,xn) for partitions κ such that |κ| ≤ N. Both algorithms have the property that for nonnegative arguments x1, . . . ,xn the output is computed to high relative accuracy and the cost per Schur function is O(n2).

We describe several classes of holomorphic functions of positive real part on the unit ball; each is characterized by an operator-valued Herglotz formula. Motivated by results of J.E. McCarthy and M. Putinar, we define a family of weighted CauchyFantappiè pairings on the ball and establish duality relations between certain pairs of classes, and in particular we identify the dual of the positive...

Jeffrey Adams, University of Maryland. The Chevalley Involution for Real Groups, with applications to the Fubini-Schur Indicator. The Chevalley involution of a complex group is unique up to conjugation, and takes any algebraic representation to its contragredient. The analogue over local fields is subtle. We prove that the Chevalley involution is defined over R, and with an appropriate conditio...

In this paper, a property of Schur polynomial of real coe cients and real Toeplitz matrix is given. Suppose that the vector of real coe cients of a Schur polynomial annihilates a real Toeplitz matrix, then the Toeplitz matrix is in fact a zero matrix.

We prove that the Lipschitz free spaces over certain types of discrete metric have Radon–Nikodým property. also show space a complete, locally compact has Schur or approximation property when

We prove that structure constants related to Hecke algebras at roots of unity are special cases of k-Littlewood-Richardson coefficients associated to a product of k-Schur functions. As a consequence, both the 3point Gromov-Witten invariants appearing in the quantum cohomology of the Grassmannian, and the fusion coefficients for the WZW conformal field theories associated to ŝu( ) are shown to b...

Let n, r ∈ N. The affine Schur algebra S̃(n, r) (of type A) over a field K is defined to be the endomorphism algebra of certain tensor space over the extended affine Weyl group of type Ar−1. By the affine Schur–Weyl duality it is isomorphic to the image of the representation map of the U(ĝl n ) action on the tensor space when K is the field of complex numbers. We show that S̃(n, r) can be defined...

We describe an active-set, dual-feasible Schur-complement method for quadratic programming (QP) with positive definite Hessians. The formulation of the QP being solved is general and flexible, and is appropriate for many different application areas. Moreover, the specialized structure of the QP is abstracted away behind a fixed KKT matrix called Ko and other problem matrices, which naturally le...