An asymptotic formula for the number of $n$-dimensional representations of $SU(3)$

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For password please contact Pieter Moree (moree@mpim...).

There are several ways to generalize the partition function $p(n)$. One of them works via group theory. Whilst the partition function $p(n)$ corresponds to the number of (inequivalent) $n$-dimensional representations of the $SU(2)$, one can consider the sequences related to general $SU(k)$. We prove an asymptotic formula for the number of $n$-dimensional representations, counted up to equivalence, of $SU(3)$. Main tools for the analytic proof are Wright’s Circle Method and the Saddle Point Method.