Vertex operators and the class algebras of symmetric groups
Abstract
We exhibit a vertex operator which implements multiplication by powersums of JucysMurphy elements in the centers of the group algebras of all symmetric groups simultaneously. The coefficients of this operator generate a representation of ${\cal W}_{1+\infty}$, to which operators multiplying by normalized conjugacy classes are also shown to belong. A new derivation of such operators based on matrix integrals is proposed, and our vertex operator is used to give an alternative approach to the polynomial functions on Young diagrams introduced by Kerov and Olshanski.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2001
 arXiv:
 arXiv:math/0102041
 Bibcode:
 2001math......2041L
 Keywords:

 Combinatorics
 EPrint:
 23 pages, LaTex. Minor typos corrected