We study power series and analyticity in the quaternionic setting. We first consider a function f defined as the sum of a power series P n∈N qnan in its domain of convergence, which is a ball B(0, R) centered at 0. At each p ∈ B(0, R), f admits expansions in terms of appropriately defined regular power series centered at p, P n∈N (q−p)bn. The expansion holds in a ball Σ(p,R− |p|) defined with r...

We present a geometric construction of a new class of hyper-Kähler manifolds with torsion. This involves the superposition of the four-dimensional hyper-Kähler geometry with torsion associated with the NS-5-brane along quaternionic planes in H k. We find the moduli space of these geometries and show that it can be constructed using the bundle space of the canonical quaternionic line bundle over...

We find a principle of harmonic analyticity underlying the quaternionic (quaternionKähler) geometry and solve the differential constraints which define this geometry. To this end the original 4n-dimensional quaternionic manifold is extended to a biharmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group...

Given a particular solution of a one-dimensional stationary Schrödinger equation this equation of second order can be reduced to a first order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or thr...

We present some striking global consequences of a model quaternionic quantum field theory which is locally complex. We show how making the quaternionic structure a dynamical quantity naturally leads to the prediction of cosmic strings and non-baryonic hot dark matter candidates. Report Number: UM–P–96/88; RCHEP 96/11. Typeset using REVTEX

We define a global horizontal 4-form on a quaternionic contact manifold and show that it is closed if and only if the torsion of the Biquard connection vanishes provided the dimension is grater than seven. This condition characterizes quaternionic contact structures which are locally qc homothetic to 3-sasakian.

We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary operators and then analyzed in terms of their generator structure. The multi–centrality and centrality assumptions are also analyzed in generator terms, and implica...

We define a complete system of invariants en,Q, n ≥ 0 for quaternionic skew-hermitian forms, which are twisted versions of the invariants en for quadratic forms. We also show that quaternionic skew-hermitian forms defined over a field of 2-cohomological dimension at most 3 are classified by rank, discriminant, Clifford invariant and Rost invariant.

The infinite-dimensional Clifford algebra has a maze of inequivalent irreducible unitary representations. Here we determine their type -real, complex or quaternionic. Some, related to the Fermi-Fock representations, do not admit any real or quaternionic structures. But there are many on L of the circle that do and which seem to have analytic meaning. Table of contents.

The papers introduces a new complex of differential forms which provides a fine resolution for the sheaf of regular functions in two quaternionic variables and the sheaf of monogenic functions in two vector variables. The paper announces some applications of this complex to the construction of sheaves of quaternionic and Clifford hyperfunctions as equivalence classes of such differential forms.