In this paper, we are mainly interested in the construction of certain Hilbert spaces of holomorphic functions on an irreducible hermitian symmatric space D = G/K on which G acts by a natural unitary representation. Our construction will produce some new irreducible representations of the simple group G. In this introduction we shall indicate the nature of our methods and results, leaving the f...

In the present paper we review in a fibre bundle context the covariant and massless canonical representations of the Poincaré group as well as certain unitary representations of the conformal group (in 4 dimensions). We give a simplified proof of the well–known fact that massless canonical representations with discrete helicity extend to unitary and irreducible representations of the conformal ...

We have previously described an embedding of the Poincaré Lie algebra into an extension of the Lie field of the group SO0(1, 4), and we used this embedding to construct irreducible representations of the Poincaré group out of representations of SO0(1, 4). Some q generalizations of these results have been obtained by us i.e. we embed classical structures into quantum structures. Here we report o...

Let G be a noncompact simple Lie group with finite center, let K be a maximal compact subgroup, and suppose that rank G = rank K. If G/K is not Hermitian symmetric, then a theorem of Borel and de Siebenthal gives the existence of a system of positive roots relative to a compact Cartan subalgebra so that there is just one noncompact simple root and it occurs exactly twice in the largest root. Le...

We introduce the notion of a p-adic quantum bit ( p-qubit) in context mechanics initiated and developed after seminal paper Volovich [Theor. Math. Phys. 71, 574 (1987)]. In this approach, physics takes place three-dimensional space rather than Euclidean space. Based on our prior work describing special orthogonal group [Di Martino et al., arXiv:2104.06228 [math.NT] (2021)], we outline program t...

We have previously described an embedding of the Poincaré Lie algebra into an extension of the Lie field of the group SO0(1, 4), and we used this embedding to construct irreducible representations of the Poincaré group out of representations of SO0(1, 4). Some q generalizations of these results have been obtained by us i.e. we embed classical structures into quantum structures. Here we report o...