Virasoro action on Schur function expansions, skew Young tableaux and random walks
| dc.creator | Adler, M. | |
| dc.creator | van Moerbeke, P. | |
| dc.date | 2003-09-11 | |
| dc.date.accessioned | 2026-07-07T05:01:04Z | |
| dc.date.available | 2026-07-07T05:01:04Z | |
| dc.description | It is known that some matrix integrals over U(n) satisfy an sl(2,R)-algebra of Virasoro constraints. Acting with these Virasoro generators on 2-dimensional Schur function expansions leads to difference relations on the coefficients of this expansions. These difference relations, set equal to zero, are precisely the backward and forward equations for non-intersecting random walks. The transition probabilities for these random walks appear as the coefficients of an expansion of U(n)-matrix integrals (of the type above), by inserting in the integral the product of two Schur polynomials associated with two partitions; the latter are specified by the initial and final positions of the non-intersecting random walk. An essential ingredient in this work is the generalization of the Murnaghan-Nakayama rule to the action of Virasoro on Schur polynomials. | |
| dc.description | 60 pages | |
| dc.identifier | https://arxiv.org/abs/math/0309202 | |
| dc.identifier | http://arxiv.org/abs/math/0309202 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68545 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.title | Virasoro action on Schur function expansions, skew Young tableaux and random walks | |
| dc.type | text |