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Infinite-dimensional hyperkähler manifolds associated with Hermitian-symmetric affine coadjoint orbits

Alice Barbara Tumpach (2009)

Annales de l’institut Fourier

In this paper, we construct a hyperkähler structure on the complexification 𝒪 ℂ of any Hermitian symmetric affine coadjoint orbit 𝒪 of a semi-simple L * -group of compact type, which is compatible with the complex symplectic form of Kirillov-Kostant-Souriau and restricts to the Kähler structure of 𝒪 . By a relevant identification of the complex orbit 𝒪 ℂ with the cotangent space T 𝒪 of 𝒪 induced by Mostow’s decomposition theorem, this leads to the existence of a hyperkähler structure on T 𝒪 compatible with...

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...

Introduction to quantum Lie algebras

Gustav Delius (1997)

Banach Center Publications

Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras U h ( g ) . The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. The recent general results about quantum Lie algebras are introduced with the help of the explicit example of ( s l 2 ) h .

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.

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