RESEARCH
My research interests are
primarily on the representation theories of Lie groups and Lie Algebras and on their
applications to various problems in scattering theory. My recent work deals
with the harmonic analysis of pseudo-Riemannian symmetric space and this has
enabled me to prove an extension of the uncertainty principle already proved in
a Riemannian space, Also I have studied a class of cohomological
spaces for pseudo-unitary groups in general. I am currently working on the
constructions of all indecomposable Verma modules of
the four-dimensional conformal group. The major motivation of this study is to apply
this tool to construct a model for decaying dynamical systems. I am also
working on the quantum deformation theory and on representations of certain quantum
groups and on Hopf algebras and possibly to apply
them in problems in quantization. I list below some of my earlier works which
have received fairly good standing in citations and the main results of which also seem to
have made some break-through. Some of these results have
been obtained in collaborations with late Professor Asim
Barut of the
Invariant eigendistributions of SU(p,q).
Composition
series for analytic continuations of holomorphic
discrete series representations of SU(p,q).
Indecomposable representations of osp(2,1).
Algebraic scattering theory of relativistic composite systems.
Path integral realization of a dynamical group.
A new realization of
dynamical groups and factorization methods.
Ladder operators of group matrix elements.
Quantum theory
of infinite component fields.
Some new identities of Clebsch-Gordan coefficients and representation functions of
SO(2,1) and SO(4).
Inelastic transition form factors
in the Hydrogen atom.
The following papers will be published in the near
future:
The uncertainty principle in pseudo-Riemannian
symmetric space
Cohomological spaces for pseudo-unitary groups.
Indecomposable Verma modules of the conformal group.
Some identities involving