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Название: Noncommutative Character Theory of the Symmetric Group
Авторы: Blessenohl D., Schocker M.
Аннотация:
This set of lecture notes presents a new approach to the representation theory of the s3Tnmetric group — more precisely: to the character theory of the symmetric group over a field of characteristic zero. Knowledge of the classical theory is unnecessary — perhaps, even a hindrance to the understanding of this new theory which is in many ways more immediate, more efficient, more transparent, and more elementary due to the new tools that He behind the word "noncommutative".
The ordinary character theory of the symmetric group is a commutative theory based on the commutative algebra of class functions or, equivalently, the algebra of symmetric functions. The monographs of James and Kerber and of Macdonald are general references on the subject.
The noncommutative character theory is based on a noncommutative algebra which maps onto the algebra of class functions. The underlying idea is to transfer problems to the noncommutative superstructure, and to solve them in that setting.