相关论文: On the spectra of hypermatrix direct sum and Krone…

We disprove the sum-product conjecture for real numbers by constructing arbitrarily large $A\subset \mathbb{R}$ (whose elements are algebraic integers in a number field of degree $\asymp \log\lvert A\rvert$) such that \[\max(\lvert…

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations. Then we study their behaviour under the…

Here, we suggest a method to represent general directed uniform and non-uniform hypergraphs by different connectivity tensors. We show many results on spectral properties of undirected hypergraphs also hold for general directed uniform…

We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…

We consider a tensor product of two spaces of holomorphic functions on a Hermitian symmetric space of tube type. Then generically this is decomposed into a direct sum of irreducible subrepresentations. In this manuscript, we construct the…

In this paper we obtain the Wedderburn-Artin decomposition of a semisimple group algebra associated to a direct product of finite groups. We also provide formulae for the number of all possible group codes, and their dimensions, that can be…

Products and sums of random matrices have seen a rapid development in the past decade due to various analytical techniques available. Two of these are the harmonic analysis approach and the concept of polynomial ensembles. Very recently, it…

We give a direct combinatorial proof that the product of two descent classes in a symmetric group is a sum of descent classes. The proof is based on the fact that the group product gives a covering map when descent classes are endowed with…

We calculate all decomposition matrices of the cyclotomic Hecke algebras of the rank 2 exceptional complex reflection groups in characteristic 0. We prove the existence of canonical basic sets in the sense of Geck-Rouquier and show that all…

The primary objective of this paper is to generalize the results of [arXiv:2111.03548] to the case of quasi-smooth Berkovich curves by establishing a connection between the spectrum and the radii of convergence. To achieve this, we…

Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from non-commutative harmonic analysis, ergodic…

We study the direct sum of q-matroids by way of their cyclic flats. Using that the rank function of a q-matroid is fully determined by the cyclic flats and their ranks, we show that the cyclic flats of the direct sum of two q-matroids are…

A technique to compute arbitrary products of a class of Fibonacci $2\times2$ square matrices is proved in this work. General explicit solutions for non autonomous Fibonacci difference equations are obtained from these products. In the…

We present explicit descriptions of the decompositions of vertices of a hypercube graph with respect to its distinguished symmetric cycle.

We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…

We derive an explicit expression for an associative star product on non-commutative versions of complex Grassmannian spaces, in particular for the case of complex 2-planes. Our expression is in terms of a finite sum of derivatives. This…

We review known factorization results in quaternion matrices. Specifically, we derive the Jordan canonical form, polar decomposition, singular value decomposition, the QR factorization. We prove there is a Schur factorization for commuting…

Starting with a spectral triple on a unital $C^{*}$-algebra $A$ with an action of a discrete group $G$, if the action is uniformly bounded (in a Lipschitz sense) a spectral triple on the reduced crossed product $C^{*}$-algebra $A\rtimes_{r}…

This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields.…

This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex…