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      Multiplicity formulas for fundamental strings of representations of classical Lie algebras

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          Abstract

          We call the \emph{\(p\)-fundamental string} of a complex simple Lie algebra to the sequence of irreducible representations having highest weights of the form \(k\omega_1+\omega_p\) for \(k\geq0\), where \(\omega_j\) denotes the \(j\)-th fundamental weight of the associated root system. For a classical complex Lie algebra, we establish a closed explicit formula for the weight multiplicities of any representation in any \(p\)-fundamental string.

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          Young-diagrammatic methods for the representation theory of the classical groups of type Bn, Cn, Dn

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            SINGULAR REDUCTION AND QUANTIZATION

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              A formula for the multiplicity of a weight

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                Author and article information

                Journal
                2017-06-23
                Article
                1706.07839
                3a0bc325-7765-407b-9b97-429acca9a8cf

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

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                Custom metadata
                17B10, 17B22, 22E46
                math.RT

                Algebra
                Algebra

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