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Integrable models of interaction of matter with radiation.

Inozemtsev, Vladimir I., Inozemtseva, Natalia G. (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Integrable string models in terms of chiral invariants of $S U (n), S O (n), S P (n)$ groups.

Gershun, Victor D. (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Internal Symmetries and Additional Quantum Numbers for Nanoparticles

V.G. Yarzhemsky (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

Wavefunctions of symmetrical nanoparticles are considered making use of induced representation method. It is shown that when, at the same total symmetry, the order of local symmetry group decreases, additional quantum numbers are required for complete labelling of electron states. It is shown that the labels of irreducible representations of intermediate subgroups can be used for complete classification of states in the case of repeating IRs in symmetry adapted linear combinations. The intermediate...

Invariant symbolic calculus for compact Lie groups

Benjamin Cahen (2019)

Archivum Mathematicum

We study the invariant symbolic calculi associated with the unitary irreducible representations of a compact Lie group.

Invariant symbolic calculus for semidirect products

Benjamin Cahen (2018)

Commentationes Mathematicae Universitatis Carolinae

Let $G$ be the semidirect product $V ⋊ K$ where $K$ is a connected semisimple non-compact Lie group acting linearly on a finite-dimensional real vector space $V$ . Let $π$ be a unitary irreducible representation of $G$ which is associated by the Kirillov-Kostant method of orbits with a coadjoint orbit of $G$ whose little group is a maximal compact subgroup of $K$ . We construct an invariant symbolic calculus for $π$ , under some technical hypothesis. We give some examples including the Poincaré group.