Related papers: An Explicit Construction of Casimir Operators and …
In this paper we discuss applications of the geometric theory of composition operators on Sobolev spaces to the spectral theory of non-linear elliptic operators. The lower estimates of the first non-trivial Neumann eigenvalues of the…
We give an explicit quantum super field construction of the N=2 super Casimir WA(n)-algebras, which is obtained from supersymmetric Miura transformation for the Lie superalgebra A(n,n-1). And also we give an extension of this algebra…
In this paper we classify the irreducible quasifinite highest weight modules over the orthogonal and symplectic types Lie subalgebras of the Lie algebra of the matrix quantum pseudo differential operators. We also realize them in terms of…
An Ore extension over a polynomial algebra F[x] is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra A_h generated by elements x,y, which satisfy yx-xy = h, where h is in F[x]. When h is…
We compute the isomorphism class in $\mathfrak{KK}^{alg}$ of all noncommutative generalized Weyl algebras $A=\CC[h](\sigma, P)$, where $\sigma(h)=qh+h_0$ is an automorphism of $\CC[h]$, except when $q\neq 1$ is a root of unity. In…
In this short note, we provide OPEs for several affine W-algebras associated with Lie algebras of rank two and give some direct applications.
We show that permutation weights, which are previously introduced for finite Lie algebras, can be appropriately defined also for affine Lie algebras. This allows us to classify all the weights of an affine Weyl orbit explicitly. Let…
We consider $\ell^r$ extensions of Calderon-Zygmund operators on weighted spaces $L^p(w)$ with $w$ an $A_p$ weight and $1 < p < \infty$. We give quantitative estimates of these operators' norm in terms of a given weight's $A_p$…
We describe co-adjoint orbits and Casimir functions for two-step free-nilpotent Lie algebras. The symplectic foliation consists of affine subspaces of the Lie coalgebra of different dimensions. Further, we consider left-invariant…
In this paper, we exhibit explicitly a sequence of $2\times2$ matrix valued orthogonal polynomials with respect to a weight $W_{p,n}$, for any pair of real numbers $p$ and $n$ such that $0<p<n$. The entries of these polynomiales are…
We construct a flat connection on the elliptic configuration space associated to any complex semisimple Lie algebra g. This elliptic Casimir connection has logarithmic singularities, and takes values in the deformed double current algebra…
Conditions for the construction of polynomial eigen--operators for the Hamiltonian of collective string field theories are explored. Such eigen--operators arise for only one monomial potential $v(x) = \mu x^2$ in the collective field…
Several issues concerning quantum kappa-Poincare algebra are discussed and reconsidered here. We propose two different formulations of kappa-Poincare quantum algebra. Firstly we present a complete Hopf algebra formulae of kappa-Poincare in…
We classify Lie-Poisson brackets that are formed from Lie algebra extensions. The problem is relevant because many physical systems owe their Hamiltonian structure to such brackets. A classification involves reducing all brackets to a set…
Calogero-Sutherland models associated to the Weyl groups of type A and B with exchange terms included in the Hamiltonians systems have non-symmetric eigenfunctions, which are products of the ground state with members of a family of…
We describe an algorithm to count the number of distinct real zeros of a polynomial (square) system f. The algorithm performs O(n D kappa(f)) iterations where n is the number of polynomials (as well as the dimension of the ambient space), D…
For every uncountable cardinal $\kappa$ there are $2^\kappa$ nonisomorphic simple AF algebras of density character $\kappa$ and $2^\kappa$ nonisomorphic hyperfinite II$_1$ factors of density character $\kappa$. These estimates are maximal…
We consider operators of the form $\mathbf{T}=\mathbf{A^*}(V\mu)\mathbf{A}$ in $\mathbb{R}^\mathbf{N}$, where $\mathbf{A}$ is a pseudodifferential operator of order $-l$, $\mu$ is a compactly supported singular measure, order $s>0$…
We construct characteristic identities for the split (polarized) Casimir operators of the simple Lie algebras in defining (minimal fundamental) and adjoint representations. By means of these characteristic identities, for all simple Lie…
This work develops a magnetic pseudodifferential calculus for super operators OpA(F); these map operators onto operators (as opposed to Lp functions onto Lq functions). Here, F could be a tempered distribution or a H\"ormander symbol. An…