Traces on Infinite-Dimensional Brauer Algebras

A. M. Vershik ; P. P. Nikitin

Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 3-11.

Résumé

We prove a theorem describing central measures for random walks on graded graphs. Using this theorem, we obtain the list of all finite traces on three infinite-dimensional algebras, namely, on the Brauer algebra, the walled Brauer algebra, and the partition algebra. The main result is that these lists coincide with the list of traces of the symmetric group or (for the walled Brauer algebra) of the square of the symmetric group.

Détail

Keywords: Brauer algebra, walled Brauer algebra, central measure, finite trace.
Mots-clés : partition algebra

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