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Noncommutative Schur functions and their applications. (English) Zbl 1011.05062
Summary: We develop a theory of Schur functions in noncommuting variables, assuming commutation relations that are satisfied in many well-known associative algebras. As an application of our theory, we prove Schur-positivity and obtain generalized Littlewood-Richardson and Murnaghan-Nakayama rules for a large class of symmetric functions, including stable Schubert and Grothendieck polynomials.

MSC:
05E05 Symmetric functions and generalizations
20C30 Representations of finite symmetric groups
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