Factorization problems in complex reflection groups
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866910319125725184 |
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| author | Lewis, Joel Brewster Morales, Alejandro H. |
| author_facet | Lewis, Joel Brewster Morales, Alejandro H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_11961 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Factorization problems in complex reflection groups Lewis, Joel Brewster Morales, Alejandro H. Combinatorics Representation Theory 20F55, 05E10, 05A15 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. |
| title | Factorization problems in complex reflection groups |
| topic | Combinatorics Representation Theory 20F55, 05E10, 05A15 |
| url | https://arxiv.org/abs/1906.11961 |