A note on Franel numbers and $SU(3)$
Jos\'e Fern\'andez N\'u\~nez, Wifredo Garc\'ia Fuertes, Askold M., Perelomov
TL;DR
This paper explores the relationship between Franel numbers and weight multiplicities in tensor powers of the adjoint representation of SU(3), providing new insights into their combinatorial and representation-theoretic connections.
Contribution
It establishes a novel link between Franel numbers and the multiplicities in tensor powers of SU(3)'s adjoint representation.
Findings
Identifies a connection between Franel numbers and SU(3) weight multiplicities.
Provides formulas relating combinatorial numbers to representation theory.
Enhances understanding of tensor product decompositions in SU(3).
Abstract
We study weight multiplicities in tensor powers of the adjoint representation of and relate them to Franel numbers.
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