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Communication Dans Un Congrès Année : 2018

Cyclotomic shuffles

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). 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 of the 1-shuffle analogue in the cyclotomic Hecke algebra H(m, 1, n) for m = 2 and small n.
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Dates et versions

hal-01777546 , version 1 (24-04-2018)

Identifiants

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Oleg Ogievetsky, Varvara Petrova. Cyclotomic shuffles. 12th International Workshop on Supersymmetries and Quantum Symmetries, Jul 2017, Dubna, Russia. pp.867-872, ⟨10.1134/S1063779618050325⟩. ⟨hal-01777546⟩
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