Related papers: On compositions with $x^2/(1-x)$
Let k be a field of characteristic zero. We consider graded subalgebras A of k[x_1,...,x_m]/(x_1^2,...,x_m^2) generated by d linearly independant linear forms. Representations of matroids over k provide a natural description of the…
The canonical coherent states are expressed as infinite series in powers of a complex number $z$ in their infinite series version. In this article we present classes of coherent states by replacing this complex number $z$ by other choices,…
We show that any m-isometric tuples of commuting operators on a finite dimensional Hilbert space can be decomposed as a sum of a spherical isometry and a commuting nilpotent tuple. Our approach applies as well to tuples of algebraic…
This is a note for constructing fundamental invariants and computing the Hilbert series of the invariant subalgebras of tensor products of polynomial rings under the action by a direct product of symmetric groups. Our computation relies on…
Quot schemes of quotients of a trivial bundle of arbitrary rank on a nonsingular projective surface X carry perfect obstruction theories and virtual fundamental classes whenever the quotient sheaf has at most 1-dimensional support. The…
Let F(R^n) be the algebra of Fourier transforms of functions from L_1(R^n), K(R^n) be the algebra of Fourier transforms of bounded complex Borel measures in R^n and W be Wiener algebra of continuous 2pi-periodic functions with absolutely…
This short note is a supplement to the previous article with the same title. Here we treat a conical symplectic variety obtained as a finite covering of a (not necessarily normal) nilpotent orbit closure of a complex semisimple Lie algebra.
An automorphism $u$ of a vector space is called unipotent of index $2$ whenever $(u-\mathrm{id})^2=0$. Let $b$ be a non-degenerate symmetric or skewsymmetric bilinear form on a vector space $V$ over a field $\mathbb{F}$ of characteristic…
We derive for a pair of operators on a symplectic space which are adjoints of each other with respect to the symplectic form (that is, they are sympletically adjoint) that, if they are bounded for some scalar product on the symplectic space…
The main purpose of this article is to extend some of the ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. Given a generic component of the…
In this paper, we study a Dirichlet series generated by powers of harmonic numbers. As an application of these functions, we derive certain series involving harmonic numbers. We also study the analytic properties of these Dirichlet series…
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
This article is concerned with analytic Hamiltonian dynamical systems in infinite dimension in a neighborhood of an elliptic fixed point. Given a quadratic Hamiltonian, we consider the set of its analytic higher order perturbations. We…
For families of orthogonal and symplectic types quantum matrix (QM-) algebras, we derive corresponding versions of the Cayley-Hamilton theorem. For a wider family of Birman-Murakami-Wenzl type QM-algebras, we investigate a structure of its…
A sufficient condition for the convergence of a generalized formal power series solution to an algebraic $q$-difference equation is provided. The main result leans on a geometric property related to the semi-group of (complex) power…
Recently, Herbig--Schwarz--Seaton have shown that $3$-large representations of a reductive group $G$ give rise to a large class of symplectic singularities via Hamiltonian reduction. We show that these singularities are always terminal. We…
In the Hilbert space of n qubits, we introduce the symplectic space (n odd) and the orthogonal space (n even) via the spin-flip operator. Under this mathematical structure we discuss some properties of n qubits, including homomorphically…
We present a new proof of a result due to Taubes: if X is a closed symplectic four-manifold with b_+(X) > 1+b_1(X) and with some positive multiple of the symplectic form a rational class, then the Poincare dual of the canonical class of X…
We answer a question of Oprea-Tralle on the realizability of symplectic algebras by symplectic manifolds in dimensions divisible by four, along with a question of Lupton-Oprea in all even dimensions. This will also allow us to address, in…
In this paper we study a restricted family of holomorphic symplectic leaves in the Poisson-Lie group ${\rm GL}_r(\mathcal{K}_{\mathbb{P}^1_x})$ with rational quadratic Sklyanin brackets induced by a one-form with a single quadratic pole at…