By S. V. Kerov
This e-book reproduces the doctoral thesis written by way of a awesome mathematician, Sergei V. Kerov. His premature loss of life at age fifty four left the mathematical group with an in depth physique of labor and this distinctive monograph. In it, he supplies a transparent and lucid account of effects and strategies of asymptotic illustration conception. The publication is a distinct resource of knowledge at the very important subject of present examine. Asymptotic illustration conception of symmetric teams bargains with difficulties of 2 forms: asymptotic homes of representations of symmetric teams of enormous order and representations of the proscribing item, i.e., the limitless symmetric team. the writer contributed considerably within the improvement of either instructions. His publication offers an account of those contributions, in addition to these of alternative researchers. one of the difficulties of the 1st sort, the writer discusses the houses of the distribution of the normalized cycle size in a random permutation and the restricting form of a random (with appreciate to the Plancherel degree) younger diagram. He additionally reports stochastic houses of the deviations of random diagrams from the restricting curve. one of the difficulties of the second one style, Kerov reviews a massive challenge of computing irreducible characters of the limitless symmetric crew. This results in the examine of a continuing analog of the idea of younger diagram, and particularly, to a continual analogue of the hook stroll set of rules, that is renowned within the combinatorics of finite younger diagrams. In flip, this development presents a very new description of the relation among the classical second difficulties of Hausdorff and Markov. The booklet is appropriate for graduate scholars and examine mathematicians drawn to illustration concept and combinatorics.
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