Counter-example to conjectured SU(N) character asymptotics

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We give a counterexample to the large $N$ asymptotics of character values $χ_R(U)$ of irreducible characters of SU(N) conjectured in papers of Gross-Matytsin and Kazakov-Wynter in 1995. Our counterexample is based on Kostant's calculation of values of SU(N) characters on Coxeter elements.
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