Related papers: Classification of positive energy representations …
We show that every unitary positive energy representation W of the Virasoro algebra exponentiates to a holomorphic *-representation of the semigroup of annuli by bounded operators on the Hilbert space completion of W. We use this to show…
We give the classification of the positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n,R).
In this manuscript, we give a classification of all irreducible, unitary representations of complex spin groups.
We give a constructive classification of the positive energy (lowest weight) unitary irreducible representations of the D=6 superconformal algebras osp(8*/2N). Our results confirm all but one of the conjectures of Minwalla (for N=1,2) on…
We continue the study of positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n,R). We present the full list of these UIRs. We give the Proof of the case osp(1|8,R).
We present the list of irreducible (generalized) highest weight modules over the Virasoro algebra and N=1 super-Virasoro algebras obtained as factor-modules of (generalized) Verma modules. We present also the character formulae of all these…
We give expressions for the singular vectors in the highest weight representations of the Virasoro algebra. We verify that the expressions --- which take the form of a product of operators applied to the highest weight vector --- do indeed…
We continue the study of positive energy (lowest weight) unitary irreducible representations of the superalgebras $osp(1|2n,R)$. We update previous results and present the full list of these UIRs. We give also some character formulae for…
We classify and construct all irreducible positive energy representations of the loop group of a compact, connected and simple Lie group and show that they admit an intertwining action of Diff(S^{1}).
Let G be a semi-simple non-compact Lie group with unitary lowest/highest weight representations. We consider explicitly the relation between three types of representations of G: positive energy (unitary lowest weight)representations,…
We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…
In this paper, we classify all irreducible weight modules with finite-dimensional weight spaces over the affine-Virasoro Lie algebra of type $A_1$.
We construct projective unitary representations of the smooth Deligne cohomology group of a compact oriented Riemannian manifold of dimension 4k+1, generalizing positive energy representations of the loop group of the circle. We also…
This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.
We explicitly demonstrate that the unitary representations of the $w_\infty$ algebra and its truncations are just the unitary representations of the Virasoro algebra.
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
We compute the fusion rings of positive energy representations of the loop groups of the simple, simply connected Lie groups.
We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex…
In this paper it is proved that an irreducible weight module with finite-dimensional weight spaces over the Schr\"{o}dinger-Virasoro algebras is a highest/lowest weight module or a uniformly bounded module. Furthermore, indecomposable…
We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.