Transitive powers of Young-Jucys-Murphy elements are central
| dc.creator | Goulden, I. P. | |
| dc.creator | Jackson, D. M. | |
| dc.date | 2007-04-09 | |
| dc.date.accessioned | 2026-07-07T07:55:44Z | |
| dc.date.available | 2026-07-07T07:55:44Z | |
| dc.description | Although powers of the Young-Jucys-Murphya elements X_i = (1 i) + ... +(i-1 i), i = 1, ..., n, in the symmetric group S_n acting on {1, ...,n} do not lie in the centre of the group algebra of S_n, we show that transitive powers, namely the sum of the contributions from elements that act transitively on {1, >...,n}, are central. We determine the coefficients, which we call star factorization numbers, that occur in the resolution of transitive powers with respect to the class basis of the centre of S_n, and show that they have a polynomiality property. These centrality and polynomiality properties have seemingly unrelated consequences. First, they answer a question raised by Pak about reduced decompositions; second, they explain and extend the beautiful symmetry result discovered by Irving and Rattan; and thirdly, we relate the polynomiality to an existing polynomiality result for a class of double Hurwitz numbers associated with branched covers of the sphere, which therefore suggests that there may be an ELSV-type formula associated with the star factorization numbers. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/0704.1100 | |
| dc.identifier | http://arxiv.org/abs/0704.1100 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127073 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 05E99, 14H10 | |
| dc.title | Transitive powers of Young-Jucys-Murphy elements are central | |
| dc.type | text |