C. D. da Fonseca

collaborators

5 papers

math.CA2024

$a$ -potent Schwarz matrices and Bessel-like Jacobi polynomials

Alexander Dyachenko, Carlos M. da Fonseca, Mikhail Tyaglov

We consider the problem of the reconstruction of a Schwarz matrix from exactly one given eigenvalue. This inverse eigenvalue problem leads to the Jacobi orthogonal polynomials~$\{P…

math.RT2024

Gelfand-Tsetlin modules for Lie algebras of rank $2$

Milica Anđelić, Carlos M. da Fonseca, Vyacheslav Futorny +1

We explicitly construct families of simple modules for Lie algebras of rank $2$ , on which certain commutative subalgebra acts diagonally and has a simple spectrum. In type $A$ thes…

math.RT2016

Topological classification of systems of bilinear and sesquilinear forms

Carlos M. da Fonseca, Vyacheslav Futorny, Tetiana Rybalkina +1

Let $A$ and $B$ be two systems consisting of the same vector spaces $C^{n_{1}}, \dots, C^{n_{t}}$ and bilinear or sesquilinear forms $A_i,B_i:\mathbb C^{n_{k(i)…

math.CO2016

The $μ$ -permanent, a new graph labeling, and a known integer sequence

Milica Anđelić, Carlos M. da Fonseca, António Pereira

Let $A = (a_{ij})$ be an $n$ -by- $n$ matrix. For any real number $μ$ , we define the polynomial $P_{μ} (A) = σ \in S_{n} \sum a_{1 σ (1)} \dots a_{nσ (n)} μ^{ℓ (σ)},$ as the $μ$ -permane…

math.NT2016

Basic trigonometric power sums with applications

Carlos M. da Fonseca, M. Lawrence Glasser, Victor Kowalenko

We present the transformation of several sums of positive integer powers of the sine and cosine into non-trigonometric combinatorial forms. The results are applied to the derivatio…

a-potent Schwarz matrices and Bessel-like Jacobi polynomials

Gelfand-Tsetlin modules for Lie algebras of rank 2

Topological classification of systems of bilinear and sesquilinear forms

The μ-permanent, a new graph labeling, and a known integer sequence

Basic trigonometric power sums with applications

$a$ -potent Schwarz matrices and Bessel-like Jacobi polynomials

Gelfand-Tsetlin modules for Lie algebras of rank $2$

The $μ$ -permanent, a new graph labeling, and a known integer sequence