Symmetric functions are vital to the study of combinatorics because they provide valuable information about partitions and permutations, topics which constitute the core of the subject. The significance of symmetric function theory is manifest by its connections to other branches of mathematics, including group theory, representation theory, Lie algebras, and algebraic geometry. One important b...

Various properties of Banach spaces, including the reeexivity and the Schur property of a space, are characterized in terms of properties of corresponding classes of locally Lipschitz functions on those spaces.

we study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic thom forms and distributional thom currents, dual to different types of submanifolds. we show that the harmonic thom form associated to a symplectic submanifold is nowhere vanishing. we also construct symplectic smoothing operators which preserve the harmonicity of distri...

We prove Okounkov’s conjecture, a conjecture of Fomin-FultonLi-Poon, and a special case of Lascoux-Leclerc-Thibon’s conjecture on Schur positivity and give several more general statements using a recent result of Rhoades and Skandera. We include an alternative derivation of this result directly from Haiman’s work on Schur positive immanants. Our results imply an intriguing log-concavity propert...

In this paper, we investigate the super RSK correspondence, first introduced by Pak and Postnikov (1994), which generalizes both the RSK correspondence and the dual RSK correspondence. The bijection relates objects that are known as oscillating supertableau and (intransitive) supergraphs. We prove a number of theorems that were stated in the original paper of Pak and Postnikov, but whose proofs...

It is well known that a generalized q-Schur algebra may be constructed as a quotient of a quantized enveloping algebra U or its modified form U̇. On the other hand, we show here that both U and U̇ may be constructed within an inverse limit of a certain inverse system of generalized q-Schur algebras. Working within the inverse limit Û clarifies the relation between U̇ and U. This inverse limit is a...

This paper offers a resolution to an extensively studied question in theoretical economics: which measure spaces are suitable for modeling many economic agents? We propose the condition of “nowhere equivalence” to characterize those measure spaces that can be effectively used to model the space of many agents. In particular, this condition is shown to be more general than various approaches tha...

In this paper a study of the coupling between integral equations and nite element methods is presented for two problems of propagation in frequency domain. It is shown that these problems can be viewed as multidomain problems and treated by the mean of the Schur complement technique. The complement coming from the integral equation part is expressed with the integral operators of the scattering...