Related papers: About the Dedekind psi function in Pauli graphs
We show the equivalence of the Pieri formula for flag manifolds and certain identities among the structure constants, giving new proofs of both the Pieri formula and of these identities. A key step is the association of a symmetric function…
The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…
We find certain functional identities for the Gauss q-power function of a sum of q-commuting variables. Then we use these identities to obtain two-parameter twists of the quantum affine algebra U_q (\hat{sl}_2) and of the Yangian Y(sl_2).…
Hickerson made an explicit formula for Dedekind sums $s(p,q)$ in terms of the continued fraction of $p/q$. We develop analogous formula for generalized Dedekind sums $s_{i,j}(p,q)$ defined in association with the $x^{i}y^{j}$-coefficient of…
For any $m \ge 1$ and odd prime power $\mathtt{q}=\mathtt{p}^m$, for $\mathtt{q}=2$, and for any $n \ge 1$, we show a result of decomposition for Pauli groups $\mathcal{P}_{n,\mathtt{q}}$ in terms of weak central products. This can be used…
In 1857 Sylvester established an elegant theory that certain counting functions (which he termed denumerants) are quasi-polynomials by decomposing them into periodic and non-periodic parts. Each component of the decomposition, called a…
We present the first detailed study of the kinematics of free relativistic particles whose symmetries are described by a quantum deformation of the de Sitter algebra, known as $q$-de Sitter Hopf algebra. The quantum deformation parameter is…
Dedekind sums occur in the transformation behaviour of the logarithm of the Dedekind eta-function under substitutions from the modular group. In 1892, Dedekind showed a reciprocity relation for the Dedekind sums. Apostol generalized…
The incompatibility of measurements is the key feature of quantum theory that distinguishes it from the classical description of nature. Here, we consider groups of d-outcome quantum observables with prime d represented by non-Hermitian…
The Heisenberg algebra is first deformed with the set of parameters ${q, l, \lambda}$ to generate a new family of generalized coherent states. In this framework, the matrix elements of relevant operators are exactly computed. A proof on…
Matrix elements and spherical functions of irreducible representations of the de Sitter group are studied on the various homogeneous spaces of this group. It is shown that a universal covering of the de Sitter group gives rise to quaternion…
We study quantum field theory on a de Sitter spacetime dS$_{d+1}$ background. Our main tool is the Hilbert space decomposition in irreducible unitary representations of its isometry group $SO(d+1,1)$. As the first application of the Hilbert…
This is the second paper in a series where we study arithmetic applications of the multiple elliptic Gamma functions originated in mathematical physics. In the first article in this series we defined geometric families of these functions…
For a simple connected graph $G$, the $Q$-generating function of the numbers $N_k$ of semi-edge walks of length $k$ in $G$ is defined by $W_Q(t)=\sum\nolimits_{k = 0}^\infty {N_k t^k }$. This paper reveals that the $Q$-generating function…
The method of group quantization described in the preceeding paper I is extended so that it becomes applicable to some parametrized systems that do not admit a global transversal surface. A simple completely solvable toy system is studied…
The new method of multivariate data analysis based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. We considered Schmidt formalism application to problems of statistical…
We realize some powers of Dedekind $\eta$-function as traces on quantum coordinate algebras.
Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…
We explicitly construct two classes of infinitly many commutative operators in terms of the deformed W-algebra $W_{qt}(sl_N^)$, and give proofs of the commutation relations of these operators. We call one of them local integrals of motion…
The structure of certain types of quasi shift-invariant spaces, which take the form $V(\psi,\mathcal{X}):=\overline{\text{span}}^{L_2}\{\psi(\cdot-x_j):j\in\mathbb{Z}\}$ for a discrete set $\mathcal{X}=(x_j)\subset\mathbb{R}$ is…