Geodesic
Traces on Infinite-Dimensional Brauer Algebras
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 3-11

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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.
Keywords: Brauer algebra, walled Brauer algebra, central measure, finite trace.
Mots-clés : partition algebra 
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A. M. Vershik; P. P. Nikitin. Traces on Infinite-Dimensional Brauer Algebras. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 3-11. http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a1/