Shuffle analogues for complex reflection groups G(m, 1, n)
Résumé
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). We report on the spectrum of the 1-shuffle analogue in the cyclotomic Hecke algebra H(m, 1, n) for m = 2 and small 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.
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Shuffle_analogues_for_Gm1n_groups_mémoire_M2_Petrova.pdf (2.33 Mo)
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