Virasoro action on Schur function expansions, skew Young tableaux and random walks
Adler, M. ; van Moerbeke, P.
arXiv, 0309202 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-09-11
Classification:  Mathematics - Probability,  Mathematical Physics 
@article{0309202,
     author = {Adler, M. and van Moerbeke, P.},
     title = {Virasoro action on Schur function expansions, skew Young tableaux and
  random walks},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0309202}
}

Adler, M.; van Moerbeke, P. Virasoro action on Schur function expansions, skew Young tableaux and
  random walks. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0309202/