Related papers: Eigenvalues, invariant factors, highest weights, a…

Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor…

Consider a deterministic self-adjoint matrix X_n with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limiting measure. We perturb this matrix by…

A pleasant family of graphs defined by Godsil and McKay is shown to have easily computed eigenvalues in many cases.

We consider the interplay of point counts, singular cohomology, \'etale cohomology, eigenvalues of the Frobenius and the Grothendieck ring of varieties for two families of varieties: spaces of rational maps and moduli spaces of marked,…

We present broadly applicable tools for determining the behavior of eigenvalues and eigenvectors under the addition of self-adjoint operators and under the multiplication of unitaries, in finite-dimensional Hilbert spaces. The new tools…

We give a nonrecursive, combinatorial characterization of multiplicity-free products of Grassmannian Schubert classes. This answers a question of W. Fulton and extends results of J. Stembridge.

For any finite abelian group G, the equivariant Gromov-Witten invariants of C^r/G can be viewed as a certain kind of abelian Hurwitz-Hodge integrals. In this note, we use Tseng's orbifold quantum Riemann-Roch theorem to express this kind of…

This paper presents a novel framework for tensor eigenvalue analysis in the context of multi-modal data fusion, leveraging topological invariants such as Betti numbers. Traditional approaches to tensor eigenvalue analysis often extend…

A convolution representation of continuous translation invariant and SO(n) equivariant Minkowski valuations is established. This is based on a new classification of translation invariant generalized spherical valuations. As applications,…

In this paper, we continue our study of the Hilbert polynomials of coinvariants begun in our previous work math.QA/0205324 (paper I). We describe the sl_n-fusion products for symmetric tensor representations following the method of Feigin…

This work concerns the global minimization of a prescribed eigenvalue or a weighted sum of prescribed eigenvalues of a Hermitian matrix-valued function depending on its parameters analytically in a box. We describe how the analytical…

We find conditions such that cup products induce isomorphisms in low degrees for extensions between stable polynomial representations of the general linear group. We apply this result to prove generalizations and variants of the Steinberg…

This paper collates, presents, and expands upon technology and results obtained as part of the author's PhD thesis. We generalize work done in the $\sigma$-finite setting by the author, Goldbring, Hart, and Sinclair by producing a language…

Let $G$ be a simple graph with the Laplacian matrix $L(G)$ and let $e(G)$ be the number of edges of $G$. A conjecture by Brouwer and a conjecture by Grone and Merris state that the sum of the $k$ largest Laplacian eigenvalues of $G$ is at…

Morphisms between tensor products of fundamental representations of the quantum group of sl(n) are described by the sl(n)-webs of Cautis-Kamnitzer-Morrison. Using these webs, we provide an explicit, root-theoretic formula for the local…

A new type of quadrature is developed. The Gaussian quadrature, for a given measure, finds optimal values of a function's argument (nodes) and the corresponding weights. In contrast, the Lebesgue quadrature developed in this paper, finds…

We consider several extensions of the Maillet determinant studied by Malo, Turnbull, and Carlitz and Olson, and derive properties of the underlying matrices. In particular, we compute the eigenvectors and eigenvalues of these matrices,…

Consider a $n\times n$ sparse non-Hermitian random matrix $X_n$ defined as the Hadamard product between a random matrix with centered independent and identically distributed entries and a sparse Bernoulli matrix with success probability…

Let R be a Henselian discrete valuation ring with field of fractions K. If X is a smooth variety over K and G a torus over K, then we consider X-torsors under G. If XX/R is a model of X then, using a result of Brahm, we show that X-torsors…

We study pairs of matrices $A,B\in GL_n({\mathbb C})$ such that the eigenvalues of $A$, of $B$ and of the product $AB$ are specified in advance. We show that the space of such pairs $(A,B)$ under simultaneous conjugation has dimension…