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      Splints of root systems on Lie Superalgebras

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          Abstract

          This paper classifies the splints of the root system of classical Lie superalgebras as a superalgebraic conversion of the splints of classical root systems. It can be used to derive branching rules, which have potential physical application in theoretical physics.

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          Splints of classical root systems

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            Recursion relations and branching rules for simple Lie algebras

            The branching rules between simple Lie algebras and its regular (maximal) simple subalgebras are studied. Two types of recursion relations for anomalous relative multiplicities are obtained. One of them is proved to be the factorized version of the other. The factorization property is based on the existence of the set of weights \(\Gamma\) specific for each injection. The structure of \(\Gamma\) is easily deduced from the correspondence between the root systems of algebra and subalgebra. The recursion relations thus obtained give rise to simple and effective algorithm for branching rules. The details are exposed by performing the explicit decomposition procedure for \(A_{3} \oplus u(1) \to B_{4}\) injection.
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              Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs

              , , (2012)
              We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie groups. As an application of our formulas, we recover the Theta correspondence for compact dual pairs. Along the way we give an explicit description of the real forms of basic classical type Lie superalgebras.
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                Author and article information

                Journal
                2013-05-30
                2017-05-15
                Article
                1305.7189
                ea109eab-e5c1-4bc7-98a2-8740ed5d64f1

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                math-ph hep-th math.MP

                Mathematical physics,High energy & Particle physics,Mathematical & Computational physics

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