Related papers: Quantum variance on quaternion algebras, I
In this paper, we first introduce a quantum $n$-space with a cocommutative Hopf algebra structure. Then it is shown that to this quantum $n$-space there corresponds a derivation algebra of $\sigma$-twisted derivations related to some…
We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution graph; in fact, it reduces the computation to that for…
In this paper we discuss the existence of certain classes of cuspidal automorphic representations having non-zero Fourier coefficients for general semisimple algebraic group $G$ defined over a number field $k$ such that its Archimedean…
We construct the first examples of purely continuous, $q$-deformed Lie type locally compact quantum groups in higher rank. They arise from Drinfeld-Jimbo quantization, at unimodular deformation parameter, of the totally positive part of…
Physicists such as Green, Vanhove, et al show that differential equations involving automorphic forms govern the behavior of gravitons. One particular point of interest is solutions to $(\Delta-\lambda)u=E_{\alpha} E_{\beta}$ on an…
Let ${\mathbf U}^-_q$ be the negative half of the quantum group associated to a Kac-Moody algebra ${\mathfrak g}$, and $\underline{\mathbf U}^-_q$ the quantum group obtained by a folding of ${\mathfrak g}$. Let ${\mathbf A} = {\mathbf…
In this paper, we study quadratic forms in spaces of holomorphic cusp forms. We show, conditionally, that when two quadratic forms in Hecke eigenforms share no common diagonal terms, their inner product is expected to converge to the sum of…
The system of N scalar particles with Grassmann-valued color charges plus the color SU(3) Yang-Mills field is reformulated on spacelike hypersurfaces. The Dirac observables are found and the physical invariant mass of the system in the…
We carry out an exact quantization of a PT symmetric (reversible) Li\'{e}nard type one dimensional nonlinear oscillator both semiclassically and quantum mechanically. The associated time independent classical Hamiltonian is of non-standard…
An algebraic interpretation of the one-variable quantum $q$-Krawtchouk polynomials is provided in the framework of the Schwinger realization of $\mathcal{U}_{q}(sl_{2})$ involving two independent $q$-oscillators. The polynomials are shown…
In this paper, we use derived sheaves to study rigidity phenomena in the cotangent bundles of manifolds endowed with some locally conformally symplectic ($\frak{lcs}$) structure. Taking inspiration from the work of Guillermou, Kashiwara and…
Theta series for exceptional groups have been suggested as a possible description of the eleven-dimensional quantum supermembrane. We present explicit formulae for these automorphic forms whenever the underlying Lie group $G$ is split (or…
We show that the crossed modules and bicovariant different calculi on two Hopf algebras related by a cocycle twist are in 1-1 correspondence. In particular, for quantum groups which are cocycle deformation-quantisations of classical groups…
We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of…
We investigate the problem of defining group or loop structures on spheres, where by ''sphere'' we mean the level set q(x) = c of a general K-valued quadratic form q, for an invertible scalar c. When K is a field and q non-degenerate, then…
The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a…
One-loop theta-exact quantum corrections to the neutrino propagator are computed in noncommutative U*(1) gauge-theory based on Seiberg-Witten maps. Our closed form results show that the one-loop correction contains a hard 1/epsilon UV…
We solve the long-standing problem of variational calculus on a noncommutative space or spacetime for a significant class of models with trivial jet bundle. Our approach entails a quantum version of the Anderson variational double complex…
Many important quantum algebras such as quantum symplectic space, quantum Euclidean space, quantum matrices, $q$-analogs of the Heisenberg algebra and the quantum Weyl algebra are semi-commutative. In addition, enveloping algebras $U(L_+)$…
We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order to construct a quantum mechanics over noncommutative Heisenberg algebras. The…