We introduce weakenings of two of the more prominent open problems in the classification of C∗-algebras, namely the quasidiagonality problem and the UCT problem. We show that the a positive solution of the conjunction of the two weaker problems implies a positive solution of the original quasidiagonality problem as well as allows us to give a local, finitary criteria for the MF problem, which a...

We study the continuous time Brown-Robinson ctitious play process for non-zero sum games. We show that, in general, ctitious play cannot converge cyclically to a mixed strategy equilibrium in which both players use more than two pure strategies.

The crystal base of the modified quantized enveloping algebras of type A+∞ or A∞ is realized as a set of integral bimatrices. It is obtained by describing the decomposition of the tensor product of a highest weight crystal and a lowest weight crystal into extremal weight crystals, and taking its limit using a tableaux model of extremal weight crystals. This realization induces in a purely combi...

Based on the shifted Schensted correspondence and the shifted Knuth equivalence, a shifted analog of the Poirier-Reutenauer algebra as a higher lift of Schur’s P-functions and a right coideal subalgebra of the Poirier-Reutenauer algebra is constructed. Its close relations with the peak subalgebra and the Stembridge algebra of peak functions are also uncovered.

The nonelliptic A2-webs with k “+”s on the top boundary and 3n − 2k “−”s on the bottom boundary combinatorially model the space Homsl3(V,V) of sl3-module maps on tensor powers of the natural 3-dimensional sl3-module V, and they have connections with the combinatorics of Springer varieties. Petersen, Pylyavskyy, and Rhodes showed that the set of such A2-webs and the set of semistandard tableaux ...

We propose to prove in this paper a conjecture of R. M. Robinson which generalizes to domains of connectivity w ^ 3 a result which he proved [3] for doubly-connected domains. Let D be a finite domain of the s-plane bounded by n^2 simple, closed, disjoint analytic curves, &, • • • , Cn, whose sum we denote by C. Let z0 be a point of D. We consider the class 0 of functions F(z) in D with a t most...

We consider two theories of concatenation, F and TC, proposed by Grzegorczyk, and proofs of their mutual interpretability. We also discuss the Grzegorczyk’s project of replacing, in foundational studies, the Robinson’s Q by some variant of the theory of

Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l’Aérien (MAIAA), Département Sciences et Ingénierie de la Navigation Aérienne (SINA), École Nationale de l’Aviation Civile (ENAC), 7 avenue Edouard Belin CS 54005, 31055 Toulouse, France; [email protected] * Correspondence: [email protected]; Tel.: +33-5-6217-9503 † This paper is an extended version of our...