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The concept of tensor eigenpairs has received more researches in past decades. Recent works have paid attentions to a special class of symmetric tensors termed regular simplex tensors, which is constructed by equiangular tight frame of n +…
We prove some new properties of fidelity (transition probability) and concurrence, the latter defined by straightforward extension of Wootters notation. Choose a conjugation and consider the dependence of fidelity or of concurrence on…
We present a proof of the fact that in a symmetric monoidal category over a field of characteristic zero, objects with an invertible exterior power are rigid. As an application we prove two recent conjectures on dimensions in symmetric…
We study holomorphic spheres in certain symplectic cobordisms and derive information about periodic Reeb orbits in the concave end of these cobordisms from the non-compactness of the relevant moduli spaces. We use this to confirm the strong…
We prove \emph{the other half} of Brauer's Height Zero Conjecture in the case of principal blocks.
We present a conjecture for expressing the coefficients in the Cayley-Hamilton theorem for supermatrices in terms of supertraces. The conjecture is tested for several supermatrix dimensions and unique results are obtained. Generating…
Motivated by the symmetric version of matrix multiplication we study the plethysm $S^k(\mathfrak{sl}_n)$ of the adjoint representation $\mathfrak{sl}_n$ of the Lie group $SL_n$. In particular, we describe the decomposition of this…
We prove the Banach strong Novikov conjecture for groups having polynomially bounded higher-order combinatorial functions. This includes all automatic groups.
J.J. Schaeffer proved that for $any$ induced matrix norm and $any$ invertible $T=T(n)$ the inequality \[\left|\det T\right|\left\Vert T^{-1}\right\Vert \leq\mathcal{S}\left\Vert T\right\Vert ^{n-1}\] holds with…
Exploiting particular features of classical groups, simple constructions are given for the irreducible constituents of the tensor square of the adjoint modules and the leading terms in higher tensor powers. This provides an independent…
This paper provides a survey of results on the greatest prime factor, the number of distinct prime factors, the greatest squarefree factor and the greatest m-th powerfree part of a block of consecutive integers, both without any assumption…
We calculate the low energy effective action of massless and massive complex linear superfields coupled to a massive U(1) vector multiplet. Our calculations include superspace higher derivative corrections and therefore go beyond previous…
We propose a new approach to study plethysm coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. This allows us to explain the stability properties of plethysm and Kronecker coefficients in a…
We give a proof of a conjecture of Lehrer and Shoji regarding the occurrences of the exterior powers of the reflection representation in the cohomology of Springer fibers. The actual theorem proved is a slight extension of the original…
In this paper, we prove a structure theorem for discrete optimal transportation plans. We show that, given any pair of discrete probability measures and a cost function, there exists an optimal transportation plan that can be expressed as…
In this paper, we prove a conjecture of Schnell in the surface case.
We describe some of the determinantal ideals attached to symmetric, exterior and tensor powers of a matrix. The methods employed use elements of Zariski's theory of complete ideals and of representation theory.
An elaboration of Dempster's method of constructing belief functions suggests a broadly applicable strategy for constructing lower probabilities under a variety of evidentiary constraints.
In recent work by Reguera and Thiele and by Reguera and Scurry, two conjectures about joint weighted estimates for Calder\'on-Zygmund operators and the Hardy-Littlewood maximal function have been refuted in the one-dimensional case. One of…
We formulate Vojta's conjecture for smooth weighted projective varieties, weighted multiplier ideal sheaves, and weighted log pairs and prove that all three versions of the conjecture are equivalent. In the process, we introduce generalized…