Geodesic
Vertex operators and the class algebras of symmetric groups
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part VI, Tome 283 (2001), pp. 156-177

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We exhibit a vertex operator which implements multiplication by power-sums of Jucys–Murphy elements in the centers of the group algebras of all symmetric groups simultaneously. The coefficients of this operator generate a representation of $\mathscr W_{1+\infty}$, 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. 
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     author = {A. Lascoux and J.-Y. Thibon},
     title = {Vertex operators and the class algebras of symmetric groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {156--177},
     publisher = {mathdoc},
     volume = {283},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_283_a10/}
}
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A. Lascoux; J.-Y. Thibon. Vertex operators and the class algebras of symmetric groups. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part VI, Tome 283 (2001), pp. 156-177. http://geodesic.mathdoc.fr/item/ZNSL_2001_283_a10/