The Baire theory of category, which classifies sets into two distinct categories, is an important topic in the study of metric spaces. Many results in topology arise from category theory; in particular, the Baire categories are related to a topological property. Because the Baire Category Theorem involves nowhere dense sets in a complete metric space, this paper first develops the concepts of n...

We study the class of Banach lattices that are positively polynomially Schur. Plenty examples and counterexamples provided, lattice properties this proved, arbitrary L</mml...

Mason and Ng have given a generalization to semisimple quasiHopf algebras of Linchenko and Montgomery’s generalization to semisimple Hopf algebras of the classical Frobenius-Schur theorem for group representations. We give a simplified proof, in particular a somewhat conceptual derivation of the appropriate form of the Frobenius-Schur indicator that indicates if and in which of two possible fas...

We introduce a family of tableaux that simultaneously generalizes the tableaux used to characterize Grothendieck polynomials and k-Schur functions. We prove that the polynomials drawn from these tableaux are the affine Grothendieck polynomials and k-K-Schur functions – Schubert representatives for the K-theory of affine Grassmannians and their dual in the nil Hecke ring. We prove a number of co...

A bijective proof of the product formula for the principal specialization of super Schur functions (also called hook Schur functions) is given using the combinatorial description of super Schur functions in terms of certain tableaux due to Berele and Regev. Our bijective proof is based on the Hillman–Grassl algorithm and a modified version of Schützenberger’s jeu de taquin. We then explore the ...

We introduce the notion of quantum Schur (or q-Schur) superalgebras. These algebras share certain nice properties with q-Schur algebras such as base change property, existence of canonical Z[v, v]-bases, and the duality relation with quantum matrix superalgebra A(m|n). We also construct a cellular Q(υ)-basis and determine its associated cells, called super-cells, in terms of a Robinson–Schenste...