A Difference Formula for Tensor-power Multiplicities
Hongfei Shu, Peng Zhao, Rui-Dong Zhu, Hao Zou
TL;DR
This paper introduces a new combinatorial difference formula that connects tensor product multiplicities with occupancy coefficients, extending to branching rules and conjecturally applying to Lie superalgebras.
Contribution
A novel difference formula for tensor product multiplicities that links them to occupancy coefficients and extends to branching rules for subalgebras.
Findings
Developed a combinatorial difference formula for tensor multiplicities
Extended the method to derive branching rules for subalgebras
Conjectural application to A-type Lie superalgebras
Abstract
A novel combinatorial formula is developed for for tensor product multiplicities in representation theory. We introduce a difference formula linking these multiplicities to restricted occupancy coefficients via a shifted operator. This method is extended to derive branching rules for subalgebras and is conjecturally applied to A-type Lie superalgebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry