Related papers: Joseph-like ideals and harmonic analysis for osp(m…

In a recent paper characters and superdimension formulas were investigated for the class of representations with Dynkin labels $[0,\ldots,0,p]$ of the Lie superalgebra $osp(m|n)$. Such representations are infinite-dimensional, and of…

Let $A$ be an associative simple (central) superalgebra over ${\mathbb C}$ and $L$ an invariant linear functional on it (trace). Let $a\mapsto a^t$ be an antiautomorphism of $A$ such that $(a^t)^ t=(-1)^{p(a)}a$, where $p(a)$ is the parity…

Starting from a purely algebraic procedure based on the commutant of a subalgebra in the universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians and the constants of the motion generating a polynomial…

Let $\mathcal{A}$ denote a central hyperplane arrangement of rank $n$ in affine space $\mathbb{K}^n$ over an infinite field $\mathbb{K}$ and let $l_1,\ldots, l_m\in R:= \mathbb K[x_1,\ldots,x_n]$ denote the linear forms defining the…

We give one more interpretation of the symbolic formulae $U(-N)=U(N)$ and $Sp(-2N)=SO(2N)$ by comparing the values of certain Casimir operators in the corresponding tensor representations. We show also that such relations can be extended to…

If $Q$ is a non degenerate quadratic form on ${\bb C}^n$, it is well known that the differential operators $X=Q(x)$, $Y=Q(\partial)$, and $H=E+\frac{n}{2}$, where $E$ is the Euler operator, generate a Lie algebra isomorphic to ${\go…

Let A be an associative complex algebra and L an invariant linear functional on it (trace). Let i be an involutive antiautomorphism of A such that L(i(a))=L(a) for any a in A. Then A admits a symmetric invariant bilinear form (a, b)=L(a…

The problem of determining maximal ideals in universal affine vertex algebras is difficult for levels beyond admissible, since there are no simple character formulas which can be applied. Here we investigate when certain quotient $\mathcal…

We extend two well-known results on primitive ideals in enveloping algebras of semisimple Lie algebras, the `Irreducibility theorem' and `Duflo theorem', to much wider classes of algebras. Our general version of Irreducibility theorem says…

The Lie superalgebra q(2) and its class of irreducible representations V_p of dimension 2p (p being a positive integer) are considered. The action of the q(2) generators on a basis of V_p is given explicitly, and from here two realizations…

Using a unified and systematic scheme, the free field realization of irreducible representations of osp(2|2) is constructed. By using these realization, the correlation functions of N=2 super-conformal model based on osp(2|2) symmetry and…

In this article, we study the ideal generated by $2\times 2$ permanents of a symmetric matrix. We denote this ideal by $P_2(X)$ where $X$ is a symmetric matrix. We compute a Gr\"obner basis, dimension, depth, minimal primes, and a primary…

The goal of this note is to show that Jordan algebras and superalgebras provide an elegant and concise language for formulating quantum mechanical problems with inherent (super)conformal symmetry. The superconformal symmetries of the…

Let $f:R^m \to R$ be a smooth function such that $f(0)=0$. We give a condition on $f$ when for arbitrary preserving orientation diffeomorphism $\phi:\mathbb{R} \to \mathbb{R}$ such that $\phi(0)=0$ the function $\phi\circ f$ is right…

The observation that $n$ pairs of para-Bose (pB) operators generate the universal enveloping algebra of the orthosymplectic Lie superalgebra $osp(1/2n)$ is used in order to define deformed pB operators. It is shown that these operators are…

For each complex number $\nu$, an associative symplectic reflection algebra $\mathcal H:= H_{1,\nu}(I_2(2m+1))$, based on the group generated by root system $I_2(2m+1)$, has an $m$-dimensional space of traces and an $(m+1)$-dimensional…

An algebra homomorphism $\psi$ from the q-deformed algebra $U_q({\rm iso}_2)$ with generating elements $I$, $T_1$, $T_2$ and defining relations $[I,T_2]_q=T_1$, $[T_1,I]_q=T_2$, $[T_2,T_1]_q=0$ (where $[A,B]_q=q^{1/2}AB-q^{-1/2}BA$) to the…

The superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model in the plane were considered in the first part. Here finite-dimensional representations of the symmetry algebra of the system, called the…

We conjecture the factorized scattering description for OSP(m/2n)/OSP(m-1/2n) supersphere sigma models and OSP(m/2n) Gross Neveu models. The non-unitarity of these field theories translates into a lack of `physical unitarity' of the S…

We define a class of orthosymplectic superalgebras $osp(m;j|2n;\omega)$ which may be obtained from $osp(m|2n)$ by contractions and analytic continuations in a similar way as the orthogonal and the symplectic Cayley-Klein algebras are…