Factorization problems in complex reflection groups
Canadian journal of mathematics, Tome 73 (2021) no. 4, pp. 899-946
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We enumerate factorizations of a Coxeter element in a well-generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In the infinite families of generalized permutations, our approach is fully combinatorial. It gives results analogous to those of Jackson in the symmetric group and can be refined to encode a notion of cycle type. As one application of our results, we give a previously overlooked characterization of the poset of W-noncrossing partitions.
Mots-clés :
factorizations, complex reflection groups, wreath product, permutations
Lewis, Joel Brewster; Morales, Alejandro H. Factorization problems in complex reflection groups. Canadian journal of mathematics, Tome 73 (2021) no. 4, pp. 899-946. doi: 10.4153/S0008414X2000022X
@article{10_4153_S0008414X2000022X,
author = {Lewis, Joel Brewster and Morales, Alejandro H.},
title = {Factorization problems in complex reflection groups},
journal = {Canadian journal of mathematics},
pages = {899--946},
year = {2021},
volume = {73},
number = {4},
doi = {10.4153/S0008414X2000022X},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X2000022X/}
}
TY - JOUR AU - Lewis, Joel Brewster AU - Morales, Alejandro H. TI - Factorization problems in complex reflection groups JO - Canadian journal of mathematics PY - 2021 SP - 899 EP - 946 VL - 73 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X2000022X/ DO - 10.4153/S0008414X2000022X ID - 10_4153_S0008414X2000022X ER -
%0 Journal Article %A Lewis, Joel Brewster %A Morales, Alejandro H. %T Factorization problems in complex reflection groups %J Canadian journal of mathematics %D 2021 %P 899-946 %V 73 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X2000022X/ %R 10.4153/S0008414X2000022X %F 10_4153_S0008414X2000022X
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