On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta function

Dan Romik

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arXiv · 1503.03776

On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta function

Dan Romik

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Abstract

We derive new results about properties of the Witten zeta function associated with the group SU(3), and use them to prove an asymptotic formula for the number of n-dimensional representations of SU(3) counted up to equivalence. Our analysis also relates the Witten zeta function of SU(3) to a summation identity for Bernoulli numbers discovered in 2008 by Agoh and Dilcher. We give a new proof of that identity and show that it is a special case of a stronger identity involving the Eisenstein series.

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Dan Romik. 2015-03-12. On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta function. https://arxiv.org/abs/1503.03776

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