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Traces on infinite-dimensional Brauer algebras. (English. Russian original) Zbl 1137.20011

Funct. Anal. Appl. 40, No. 3, 165-172 (2006); translation from Funkts. Anal. Prilozh. 40, No. 3, 3-11 (2005).
Summary: 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.

MSC:

20C30 Representations of finite symmetric groups
05E10 Combinatorial aspects of representation theory
20C08 Hecke algebras and their representations
16G10 Representations of associative Artinian rings
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