相关论文: Quasi-conformal actions, quaternionic discrete ser…

After reviewing the underlying algebraic structures we give a unified realization of split exceptional groups F_{4(4)},E_{6(6)}, E_{7(7)}, E_{8(8)} and of SO(n+3,m+3) as quasiconformal groups that is covariant with respect to their…

Quaternionic formulation of D=4 conformal group and of its associated twistors and their relation to harmonic analyticity is presented. Generalization of $SL(2,\cal{C})$ to the D=4 conformal group SO(5,1) and its covering group…

We study a new class of functions that arise naturally in quaternionic analysis, we call them "quasi regular functions". Like the well-known quaternionic regular functions, these functions provide representations of the quaternionic…

Superspace is considered as space of parameters of the supercoherent states defining the basis for oscillator-like unitary irreducible representations of the generalized superconformal group SU(2m,2n/2N) in the field of quaternions H. The…

We study the minimal unitary representations of non-compact groups and supergroups obtained by quantization of their geometric realizations as quasi-conformal groups and supergroups. The quasi-conformal groups G leave generalized…

We extend the definition of Weinstein's Action homomorphism to Hamiltonian actions with equivariant moment maps of (possibly infinite-dimensional) Lie groups on symplectic manifolds, and show that under conditions including a uniform bound…

This is a brief review of the main results of our paper arXiv:1101.1759 that contains a complete global treatment of the compactified trigonometric Ruijsenaars-Schneider system by quasi-Hamiltonian reduction. Confirming previous conjectures…

Biconformal gauging of the conformal group has a scale-invariant volume form, permitting a single form of the action to be invariant in any dimension. We display several 2n-dim scale-invariant polynomial actions and a dual action. We solve…

We develop a theory of twisted actions of categorical groups using a notion of semidirect product of categories. We work through numerous examples to demonstrate the power of these notions. Turning to representations, which are actions that…

The article is devoted to holomorphic and meromorphic functions of quaternion and octonion variables. New classes of quasi-conformal and quasi-meromorphic mappings are defined and investigated. Properties of such functions such as their…

We introduce quaternionic structures on abstract GKM graphs, as the combinatorial counterpart of almost quaternionic structures left invariant by a torus action of GKM type. In the GKM$_3$ setting the 2-faces of the GKM graph can naturally…

After reviewing the algebraic structures that underlie the geometries of N=2 Maxwell-Einstein supergravity theories (MESGT) in five and four dimensions with symmetric scalar manifolds, we give a unified realization of their three…

Effective actions are derived for (2,0) and (2,1) superstrings by studying the corresponding sigma-models. The geometry is a generalisation of Kahler geometry involving torsion and the field equations imply that the curvature with torsion…

We prove that given a pseudo-Riemannian conformal structure whose conformal holonomy representation fixes a totally lightlike subspace of arbitrary dimension, there is, wrt. a local metric in the conformal class defined off a singular set,…

For a class of closed manifolds N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T*N. These restrict to homogeneous quasi-morphisms on the subgroup generated by Hamiltonians with support in a given…

Proper symmetries act on fields while pseudo-symmetries act on both fields and coupling constants. We identify the pseudo-duality groups that act as symmetries of the equations of motion of general systems of scalar and vector fields and…

We give a complete classification of the real forms of simple nonlinear superconformal algebras (SCA) and quasi-superconformal algebras (QSCA) and present a unified realization of these algebras with simple symmetry groups. This…

In this paper, we discuss certain types of conformal/anticonformal actions of the generalized quasi-dihedral group $G_{n}$ of order $8n$, for $n\geq 2$, on closed Riemann surfaces, pseudo-real Riemann surfaces and compact Klein surfaces,…

This is an expository book on unitary representations of topological groups, and of several dual spaces, which are spaces of such representations up to some equivalence. The most important notions are defined for topological groups, but a…

The family of quaternionic quasi-unitary (or quaternionic unitary Cayley--Klein algebras) is described in a unified setting. This family includes the simple algebras sp(N+1) and sp(p,q) in the Cartan series C_{N+1}, as well as many…