Multiplicity formulas for fundamental strings of representations of classical Lie algebras

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 classic...

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Bibliographic Details
Published in:arXiv.org 2017-11
Main Authors: Lauret, Emilio A, Fiorela Rossi Bertone
Format: Article
Language:English
Subjects:
Algebra
Lie groups
Quantum theory
Representations
Strings
Weight
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1706.07839