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If we take the entries of the (standard $3 \times 3$) Heisenberg group to live in the Gaussian integers $\mathbb{Z}[i]$, what is the structure of this group? Are all of its representations known?

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A quick google search produced this paper. It gives generators and relations for the Heisenberg group over rings of integers of quadratic fields and discusses its representations.

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Ah, that's a nice very recent paper, thanks. I'm for Baidu, though... –  Dr Shello Dec 17 '10 at 17:53

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