arXiv subjects

Vladimir Dobrev

Publications and source records attributed to Vladimir Dobrev.

4 recordsLinked to original sources

arXiv2019

Jordan Algebraic Interpretation of Maximal Parabolic Subalgebras : Exceptional Lie Algebras

With this paper we start a programme aiming at connecting two vast scientific areas: Jordan algebras and representation theory. Within representation theory, we focus on non-compact, real forms of semisimple Lie algebras and groups as well as on the modern theory of their induced representations, in which a central role is played by the parabolic subalgebras and subgroups. The aim of the present paper and its sequels is to present a Jordan algebraic interpretations of maximal parabolic subalgebras. In this first paper, we confine ourselves to maximal parabolic subalgebras of the non-compact real forms of finite-dimensional exceptional Lie algebras, in particular focusing on Jordan algebras of rank 2 and 3.

math.RT↗

arXiv2017

Positive Energy Unitary Irreducible Representations of the Superalgebra osp(1|8,R)

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).

math.RT↗

arXiv2011

Group-Theoretical Classification of BPS and Possibly Protected States in D=4 Conformal Supersymmetry

We give explicitly the reduction of supersymmetries of the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Further we give the classification of BPS and possibly protected states.

hep-th↗

arXiv2003

Revisiting the Quantum Group Symmetry of Diatomic Molecules

We propose a q-deformed model of the anharmonic vibrations in diatomic molecules. We analyse the applicability of the model to the phenomenological Dunham's expansion by comparing with experimental data. Our methodology involves a global consistency analysis of the parameters that determine the q-deformed system, when compared with fitted vibrational parameters to 161 electronic states in diatomic molecules. We show how to include both the positive and the negative anharmonicities in a simple and systematic fashion.

cond-mat.stat-mech↗