A note on representations of the finite Heisenberg group and sums of greatest common divisors (Q2718888)
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scientific article; zbMATH DE number 1597543
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on representations of the finite Heisenberg group and sums of greatest common divisors |
scientific article; zbMATH DE number 1597543 |
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13 May 2001
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representations of finite Heisenberg groups
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0.8801956
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0.87836623
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0.8761381
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0.8731759
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0.86398363
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A note on representations of the finite Heisenberg group and sums of greatest common divisors (English)
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The authors solve an exercise in the reviewer's book [Fourier Analysis on Finite Groups and Applications, Cambridge (1999; Zbl 0928.43001), p. 297] by finding the irreducible representations of the group of all \(3\times 3\) upper triangular matrices with one's on the diagonal and entries in the ring \(\mathbb{Z}/n\mathbb{Z}\) of integers \(\operatorname {mod} n\). They compare their results with Kirillov's orbit theory and go on to obtain an identity involving sums of powers of greatest common divisors.
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