Cyclotomic Shuffles

  title={Cyclotomic Shuffles},
  author={O. Ogievetsky and Varvara Petrova},
  journal={Physics of Particles and Nuclei},
Analogues of 1-shuffle elements for complex reflection groups of type G(m, 1, n) are introduced. A geometric interpretation for G(m, 1, n) in terms of rotational permutations of polygonal cards is given. We compute the eigenvalues, and their multiplicities, of the 1-shuffle element in the algebra of the group G(m, 1, n). Considering shuffling as a random walk on the group G(m, 1, n), we estimate the rate of convergence to randomness of the corresponding Markov chain. We report on the spectrum… 

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