Related papers: A vector space basis of the quantum symplectic sph…
A toy-model quantum system is proposed. At a given integer $N$ it is defined by the pair of $N$ by $N$ real matrices $(H,\Theta)$ of which the first item $H$ specifies an elementary, diagonalizable non-Hermitian Hamiltonian $H \neq…
We give explicit constructions of quantum symplectic affine algebras at level 1 using vertex operators.
The aim of this paper is to study the natural action of the real symplectic group, $\operatorname{Sp}(4, \mathbb{R})$, on the algebraic set of $4$-dimensional Lie algebras admitting symplectic structures and to give a complete…
Let $\Gamma=\Gamma(2n,q)$ be the dual polar graph of type $Sp(2n,q)$. Underlying this graph is a $2n$-dimensional vector space $V$ over a field ${\mathbb F}_q$ of odd order $q$, together with a symplectic (i.e. nondegenerate alternating…
Operating in the framework of `supmech' (a scheme of mechanics which aims at providing a concrete setting for the axiomatization of physics and probability theory as required in Hilbert's sixth problem; integrating noncommutative symplectic…
We show that the C*-algebra of a quantum sphere $C(S_{q}^{2n+1})$ can be realized as a groupoid C*-algebra of a groupoid which is explicitly identified and is independent of the parameter $q$.
We introduce different bases for the vector space of $\mathrm{Sp}(2)\mathrm{Sp}(1)$-invariant, translation invariant continuous valuations on the quaternionic plane and determine a complete set of kinematic formulas.
The quaternionic Grassmannian HGr(r,n) is the affine open subscheme of the ordinary Grassmannian parametrizing those 2r-dimensional subspaces of a 2n-dimensional symplectic vector space on which the symplectic form is nondegenerate. In…
This note provides a formula for the character of the Lie algebra of the fundamental group of a surface, viewed as a module over the symplectic group.
We show (Theorem 3) that the symplectic reduction of the spatial $n$-body problem at non-zero angular momentum is a singular symplectic space consisting of two symplectic strata, one for spatial motions and the other for planar motions.…
A standard bicovariant differential calculus on a quantum matrix space ${\tt Mat}(m,n)_q$ is considered. The principal result of this work is in observing that the $U_q\frak{s}(\frak{gl}_m\times \frak{gl}_n))_q$ is in fact a…
Let $K$ be an imaginary quadratic field and let $\mathcal{O}_K$ be its ring of integers. For an integral ideal $\mathfrak{n}$ of $\mathcal{O}_K$, let $\Gamma_0({\mathfrak{n}})$ be the congruence subgroup of level ${\mathfrak{n}}$ consisting…
A weight basis for each finite-dimensional irreducible representation of the orthogonal Lie algebra o(2n) is constructed. The basis vectors are parametrized by the D-type Gelfand--Tsetlin patterns. Explicit formulas for the matrix elements…
An infinite dimensional algebra which is a non-decomposable reducible representation of $su(2)$ is given. This algebra is defined with respect to two real parameters. If one of these parameters is zero the algebra is the commutative algebra…
We study two classes of quantum spheres and hyperboloids which are $*$-quantum spaces for the quantum orthogonal group $\mathcal{O}(SO_q(3))$. We construct line bundles over the quantum homogeneous space of invariant elements for the…
In the 1980s, Neumann and Zagier introduced a symplectic vector space associated to an ideal triangulation of a cusped 3-manifold, such as a knot complement. We give a geometric interpretation for this symplectic structure in terms of the…
Starting from vector fields that preserve a differential form on a Riemann sphere with Grassmann variables, one can construct a Superconformal Algebra by considering central extensions of the algebra of vector fields. In this note, the N=4…
The Hamiltoinian analysis of the vector-tensor theory of gravity is performed. The resulting geometrical dynamics is reformulated into the connection dynamics, with the real SU(2)-connection serving as one of the configuration variables.…
A generalization is provided for the notion of tags, as used in various formulations of physical scenarios. It leads to the definition of tagged vector spaces, based on a set of axioms for tags and their extractors. As an application, such…
Given a quiver, a fixed dimension vector, and a positive integer n, we construct a functor from the category of D-modules on the space of representations of the quiver to the category of modules over a corresponding Gan-Ginzburg algebra of…