Related papers: The su(1,1) Dynamical Algebra for the Generalized …
We build, using the notion of zinbiel algebra, some commutative subalgebras $C_{u,v}$ inside an algebra of formal iterated integrals. There is a quotient map from this algebra of formal iterated integrals to the algebra of motivic multiple…
We propose analogs of the generalized MICZ-Kepler system on the three-dimensional sphere and (two-sheet) hyperboloid. We then construct their energy spectra and normalized wave functions, concluding that the suggested systems are minimally…
Motivated by work of R.M. Green, we obtain a presentation of Schur algebras (both the classical and quantized versions) in terms of generators and relations. The presentation is compatible with the usual presentation of the (quantized or…
The Kantor-Koecher-Tits construction associates a Lie algebra to any Jordan algebra. We generalize this construction to include also extensions of the associated Lie algebra. In particular, the conformal realization of so(p+1,q+1)…
Recent results on the Racah algebra $\mathcal{R}_n$ of rank $n - 2$ are reviewed. $\mathcal{R}_n$ is defined in terms of generators and relations and sits in the centralizer of the diagonal action of $\mathfrak{su}(1,1)$ in…
The commutator anomalies (Schwinger terms) of current algebras in $3+1$ dimensions are computed in terms of the Wodzicki residue of pseudodifferential operators; the result can be written as a (twisted) Radul 2-cocycle for the Lie algebra…
The ({\em classical}, {\em small quantum}, {\em equivariant}) cohomology ring of the grassmannian $G(k,n)$ is generated by certain derivations operating on an exterior algebra of a free module of rank $n$ ({\em Schubert Calculus on a…
Explicit forms are given of matrix elements of generalized coherent operators based on Lie algebras su(1,1) and su(2). We also give a kind of factorization formula of the associated Laguerre polynomials.
Representation theory for the Jordanian quantum algebra U=U_h(sl(2)) is developed using a nonlinear relation between its generators and those of sl(2). Closed form expressions are given for the action of the generators of U on the basis…
A general method has been developed to solve the Schr\"odinger equation for an arbitrary derivative of the $\delta$-function potential in 1-d using cutoff regularization. The work treats both the relativistic and nonrelativistic cases. A…
This paper contains a brief sketch of some methods that can be used to obtain the Wigner function for a number of systems. We give an overview of the technique as it is applied to some simple differential systems related to diffusion…
For $A$ a $C^*$-algebra, $E_1, E_2$ two Hilbert bimodules over $A$, and a fixed isomorphism $\chi : E_1\otimes_AE_2\to E_2\otimes_AE_1$, we consider the problem of computing the $K$-theory of the Cuntz-Pimsner algebra ${\mathcal…
Given a family of stable curves, we define a sheaf of factorization algebras associated to any universal factorization algebra, and prove a gluing formula for the corresponding sheaf of chiral homology, generalizing the sheaves of vertex…
We give explicit presentations by generators and relations of certain generalized Schur algebras (associated with tensor powers of the natural representation) in types B, C, D. This extends previous results in type A obtained by two of the…
We review an exact WKB resolution method for the stationary 1D Schr\"odinger equation with a general polynomial potential. This contribution covers already published material: we supply a commented summary here, stressing a few aspects…
Using three different representations of the bicomplex numbers $T\cong Cl_{C}(1,0) \cong Cl_{C}(0,1)$, which is a commutative ring with zero divisors defined by $T={w_0+w_1 {i_1}+w_2{i_2}+w_3 {j} | w_0,w_1,w_2,w_3 \in{R}}$ where…
We describe a generalization of Hashimoto and Kurano's Cauchy filtration for divided powers algebras. This filtration is then used to provide a cellular structure for generalized Schur algebras associated to an arbitrary cellular algebra.…
Issai Schur, in his doctoral thesis (1901) introduced the Schur algebra to study the polynomial representation theory of the general linear group. He described a basis of this algebra and structure constants. Later, Miguel Mendez (2001)…
Based on the fact that the Hamiltonians of the Coulomb many-particle systems are always factorized we develop the two different approaches for analytical solution of the Schr\"{o}dinger equation written for arbitrary few- and many-particle…
We examine the Generalized K$\ddot{a}$hler Geometry of quantum N=2 superconformal WZW model on $SU(2)\times U(1)$ and relate the right-moving and left-moving Kac-Moody superalgebra currents to the Generalized K$\ddot{a}$hler Geometry data…