Related papers: The orthosymplectic supergroup in harmonic analysi…
We introduce the orthosymplectic superalgebra osp(m|2n) as the algebra of Killing vector fields on Riemannian superspace R^{m|2n} which stabilize the origin. The Laplace operator and norm squared on R^{m|2n}, which generate sl(2), are…
The orthosymplectic supergroup OSp(m|2n) and unitary supergroup U(p|q) are studied following a new approach that starts from Harish-Chandra pairs and links the sheaf-theoretical supermanifold approach of Berezin and others with the…
We study the Howe dualities involving the reductive dual pairs $(O(d),spo(2m|2n))$ and $(Sp(d),osp(2m|2n))$ on the (super)symmetric tensor of $\C^d\otimes\C^{m|n}$. We obtain complete decompositions of this space with respect to their…
It turns out that harmonic analysis on the superspace R^{m|2n} is quite parallel to the classical theory on the Euclidean space R^{m} unless the superdimension M:=m-2n is even and non-positive. The underlying symmetry is given by the…
We introduce the spinor representations for osp(m|2n). These generalize the spinors for so(m) and the symplectic spinors for sp(2n) and correspond to representations of the supergroup with supergroup pair (Spin(m) x Mp(2n),osp(m|2n)). We…
In this paper, the Dirac operator, acting on super functions with values in super spinor space, is defined along the lines of the construction of generalized Cauchy-Riemann operators by Stein and Weiss. The introduction of the superalgebra…
We study two-parameter oscillator variations of the classical theorem on harmonic polynomials, associated with noncanonical oscillator representations of sl(n) and o(n). We find the condition when the homogeneous solution spaces of the…
Coordinate atypical representation of the orthosymplectic superalgebra osp(2/2) in a Hilbert superspace of square integrable functions constructed in a special way is given. The quantum nonrelativistic free particle Hamiltonian is an…
A Schroedinger type equation on the superspace R^{D|2n} is studied, which involves a potential inversely proportional to the negative of the osp(D|2n) invariant "distance" away from the origin. An osp(2,D+1|2n) dynamical supersymmetry for…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
Topological supermatter is given by ordinary topological matter constrained by supersymmetry or graded supergroups such as OSP(2N|2N). Using results on super oscillators and lattice QFT$_{d}$, we construct a super tight binding model on…
The main aim of this article is to show some intimate relations among the following three notions: (1) the metaplectic representation of $Sp(2n,\mathbb{R})$ and its extension to some semigroups, called the Olshanski semigroup for…
We study Yang-Baxter equations with orthosymplectic supersymmetry. We extend a new approach of the construction of the spinor and metaplectic $\hat{\cal R}$-operators with orthogonal and symplectic symmetries to the supersymmetric case of…
Classical harmonic analysis says that the spaces of homogeneous harmonic polynomials (solutions of Laplace equation) are irreducible modules of the corresponding orthogonal Lie group (algebra) and the whole polynomial algebra is a free…
Given a complex orthosymplectic superspace $V$, the orthosymplectic Lie superalgebra $\mathfrak {osp}(V)$ and general linear algebra ${\mathfrak {gl}}_N$ both act naturally on the coordinate super-ring $\mathcal{S}(N)$ of the dual space of…
We give an elementary proof of the first fundamental theorem of the invariant theory for the orthosymplectic supergroup by generalising the method of Atiyah, Bott and Patodi to the supergroup context. We use methods from super-algebraic…
We explicitly compute the first and second cohomology groups of the classical Lie superalgebras $sl_{m|n}$ and $osp_{2|2n}$ with coefficients in the finite dimensional irreducible modules and the Kac modules. We also show that the second…
In this paper we give a general introduction to supersymmetric spin networks. Its construction has a direct interpretation in context of the representation theory of the superalgebra. In particular we analyze a special kind of spin networks…
We study solutions of the Bethe ansatz equations associated to the orthosymplectic Lie superalgebras $\mathfrak{osp}_{2m+1|2n}$ and $\mathfrak{osp}_{2m|2n}$. Given a solution, we define a reproduction procedure and use it to construct a…
In a previous work we established a super Schur-Weyl-Brauer duality between the orthosymplectic supergroup of superdimension $(m|2n)$ and the Brauer algebra with parameter $m-2n$. This led to a proof of the first fundamental theorem of…