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Full-Text Articles in Physical Sciences and Mathematics
Bound For The Cocharacters Of The Identities Of Irreducible Representations Of $\Mathfrak{Sl}_2(\Mathbb{C})$, Mátyás Domokos
Bound For The Cocharacters Of The Identities Of Irreducible Representations Of $\Mathfrak{Sl}_2(\Mathbb{C})$, Mátyás Domokos
Turkish Journal of Mathematics
For each irreducible finite dimensional representation of the Lie algebra $\mathfrak{sl}_2(\mathbb{C})$ of $2\times 2$ traceless matrices, an explicit uniform upper bound is given for the multiplicities in the cocharacter sequence of the polynomial identities satisfied by the given representation.
Multicomponent Fokas-Lenells Equations On Hermitian Symmetric Spaces, Vladimir Gerdjikov, Rossen Ivanov
Multicomponent Fokas-Lenells Equations On Hermitian Symmetric Spaces, Vladimir Gerdjikov, Rossen Ivanov
Articles
Multi-component integrable generalizations of the Fokas-Lenells equation, associated with each irreducible Hermitian symmetric space are formulated. Description of the underlying structures associated to the integrability, such as the Lax representation and the bi-Hamiltonian formulation of the equations is provided. Two reductions are considered as well, one of which leads to a nonlocal integrable model. Examples with Hermitian symmetric spaces of all classical series of types A.III, BD.I, C.I and D.III are presented in details, as well as possibilities for further reductions in a general form.
Cartan Involutions And Cartan Decompositions Of A Semi-Simple Lie Algebra, Ian M. Anderson
Cartan Involutions And Cartan Decompositions Of A Semi-Simple Lie Algebra, Ian M. Anderson
Tutorials on... in 1 hour or less
In this worksheet we shall review the basic definitions and properties of Cartan involutions and Cartan decompositions and illustrate these using the DifferentialGeometry software package for Lie algebras.