Related papers: Minor identities for Sklyanin determinants

In this paper, we present a method to solve the quantum marginal problem for symmetric $d$-level systems. The method is built upon an efficient semi-definite program that determines the compatibility conditions of an $m$-body reduced…

We develop a correspondence between the orbits of the group of linear symplectomorphisms of a real finite dimensional symplectic vector space in the complex Lagrangian Grassmannian and the Grassmannians of linear subspaces of the real…

In studies of quantum squeezing, the emphasis is typically placed more on specific squeezed states and their evolution rather than on the dynamical operations that could simultaneously squeeze a broader range of quantum states, regardless…

In this paper, we clarified the relationship between continued fractions, determinants, and identities, making it easier to apply these methods systematically in other settings. In particular, we studied finite continued fractions from the…

Evaluation of pfaffians arises in a number of physics applications, and for some of them a direct method is preferable to using the determinantal formula. We discuss two methods for the numerical evaluation of pfaffians. The first is…

For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…

Let X be a symplectic or odd orthogonal Grassmannian which parametrizes isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove quantum Giambelli formulas which express an arbitrary Schubert class…

We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold and recover results of…

This is the second in a series of papers on standard monomial theory and invariant theory of arc spaces. For any algebraically closed field $K$, we construct a standard monomial basis for the arc space of the Pfaffian variety over $K$. As…

This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured $4\times 4$ matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete…

We give a new proof, inspired by an argument of Atiyah, Bott and Patodi, of the first fundamental theorem of invariant theory for the orthosymplectic super group. We treat in a similar way the case of the periplectic super group. Lastly,…

A Kleinian manifold Y is a quotient of a rank-one symmetric space of non-compact type by a convex-cocompact discrete group of isometries. We describe the spectral decomposition of the space of square integrable sections of locally…

We describe the action of the symplectic group on the homogeneous space of squeezed states (quantum blobs) and extend this action to the semigroup. We then extend the metaplectic representation to the metaplectic (or oscillator) semigroup…

The existence of certain Fq-spaces of differential forms of the projective line over a field K containing Fq leads us to prove an identity linking the determinant of the Moore matrix of n indeterminates with the determinant of the Moore…

We define new invariants of 3d Calabi-Yau categories endowed with a stability structure. Intuitively, they count the number of semistable objects with fixed class in the K-theory of the category ("number of BPS states with given charge" in…

We use Kazhdan-Lusztig bases of representations of the symmetric group to express Pfaffians with entries $(a_i-a_j) h_{i+j}$. In the case where the parameters $a_i$ are specialized to successive powers of $q$, and the $h_i$ are complete…

We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in recent years, are of standard random matrix type. We exploit this to compute analytically marginals of the probability density functions. This can be done…

Let ${\mathbb F}_q$ be a finite field of characteristic two and ${\mathbb F}_q(X_1,...,X_n)$ a rational function field. We use matrix methods to obtain explicit transcendental bases of the invariant subfields of orthogonal groups and…

We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…

Let $\bigwedge_\sigma V=\bigoplus_{k\geq 0}\bigwedge_\sigma^kV$ be the quantum exterior algebra associated to a finite-dimensional braided vector space $(V,\sigma)$. For an algebra $\mathfrak{A}$, we consider the convolution product on the…