Vertex Operators and the Class Algebras of Symmetric Groups

By Alain Lascoux, Jean-Yves Thibon. 2001

65 citations recorded by the source corpus.

AbstractWe exhibit a vertex operator that implements the 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 $$\mathcal{W}_{1 + \infty } $$ , 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. Bibliography: 18 titles.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/917b663d38f922e28194d368184f0721093380c4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Alexei Borodin
2. Grigori Olshanski

In Discrete Mathematics and Combinatorics

1. Alexei Borodin
2. Grigori Olshanski
3. L. Petrov
4. Ivan Corwin
5. Vadim Gorin
6. Alexey I. Bufetov
7. Philippe Biane

In Geometry and Topology

1. Grigori Olshanski
2. Alexei Borodin
3. L. Petrov
4. Vadim Gorin
5. Ivan Corwin
6. Alexey I. Bufetov

Citations in the corpus

• Infinite-dimensional diffusions as limits of random walks on partitions (2007, methodology): “We will employ the following results proved by Lascoux and Thibon in [ LT ,”
• Gromov-Witten theory, Hurwitz theory, and completed cycles (2002, unknown): “The relationship between these two linear bases can be studied using various techniques, in particular, the methods of [29, 31, 22] can be applied.”