Complete homogeneous symmetric polynomials in Jucys-Murphy elements and the Weingarten function
| dc.creator | Novak, Jonathan | |
| dc.date | 2008-11-21 | |
| dc.date | 2008-11-24 | |
| dc.date.accessioned | 2026-07-07T10:20:10Z | |
| dc.date.available | 2026-07-07T10:20:10Z | |
| dc.description | A connection is made between complete homogeneous symmetric polynomials in Jucys-Murphy elements and the unitary Weingarten function from random matrix theory. In particular we show that $h_r(J_1,...,J_n),$ the complete homogeneous symmetric polynomial of degree $r$ in the JM elements, coincides with the $r$th term in the asymptotic expansion of the Weingarten function. We use this connection to determine precisely which conjugacy classes occur in the class basis resolution of $h_r(J_1,...,J_n),$ and to explicitly determine the coefficients of the classes of minimal height when $r < n.$ These coefficients, which turn out to be products of Catalan numbers, are governed by the Moebius function of the non-crossing partition lattice $NC(n).$ | |
| dc.description | 12 Pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0811.3595 | |
| dc.identifier | http://arxiv.org/abs/0811.3595 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174762 | |
| dc.subject | Combinatorics | |
| dc.title | Complete homogeneous symmetric polynomials in Jucys-Murphy elements and the Weingarten function | |
| dc.type | text |