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Quantum Kostka and the rank one problem for $\mathfrak{sl}_{2m}$
We give necessary and sufficient conditions to specify vector bundles of conformal blocks for $\mathfrak{sl}_{2m}$ with rectangular weights which have ranks zero, one, and larger than one. First Chern classes of rank one bundles ... Read More >
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A proof of two conjectures of Chao-Ping Chen for inverse trigonometric functions
In this paper we prove two conjectures stated by Chao-Ping Chen in [Int. Trans. Spec. Funct. 23:12 (2012), 865--873], using a method for proving inequalities of mixed trigonometric polynomial functions. Read More >
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Do $n$-Lie algebras have universal enveloping algebras
The aim of this paper is to investigate in which sense, for $n\geq 3$, $n$-Lie algebras admit universal enveloping algebras. There have been some attempts at a construction (see [10] and [5]) but after analysing those we come to ... Read More >
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The generic character table of a Sylow $p$-subgroup of a finite Chevalley group ...
Let $U$ be a Sylow $p$-subgroup of the finite Chevalley group of type $D_4$ over the field of $q$ elements, where $q$ is a power of a prime $p$. We describe a construction of the generic character table of $U$. Read More >
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Triangle-free Uniquely 3-Edge Colorable Cubic Graphs
This paper presents infinitely many new examples of triangle-free uniquely 3-edge colorable cubic graphs. The only such graph previously known was given by Tutte in 1976. Read More >
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Non-uniform non-asymptotical sharp estimate for the rate of convergence for Bern ...
We derive the non-asymptotical non-uniform sharp error estimation for Bernstein's approximation of continuous function based on the modern probabilistic apparatus. We investigate also the convergence of derivative of these pol ... Read More >
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A non-Archimedean counterpart of Johnson's theorem for discrete groups
Let $K$ be a spherically complete field with a non-Archimedean valuation. We define a new version of $K-$amenability for discrete groups and show that the Banach $K-$algebra $l^1(G)$ is amenable iff $G$ is $K-$amenable in our se ... Read More >
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Lattice Paths, Young Tableaux, and Weight Multiplicities
For $\ell \geq 1$ and $k \geq 2$, we consider certain admissible sequences of $k-1$ lattice paths in a colored $\ell \times \ell$ square. We show that the number of such admissible sequences of lattice paths is given by the sum ... Read More >
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Desingularization of complex multiple zeta-functions
We introduce the method of desingularization of multi-variable multiple zeta-functions (of the generalized Euler-Zagier type), under the motivation of finding suitable rigorous meaning of the values of multiple zeta-functions at ... Read More >
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Collision times of random walks and applications to the Brownian web
Convergence of directed forests, spanning on random subsets of lattices or on point processes, towards the Brownian web has made the subject of an abundant literature, a large part of which relies on a criterion proposed by Font ... Read More >