We introduce a generalization of K–k-Schur functions and k-Schur functions via the Pieri rule. Then we obtain the Murnaghan-Nakayama rule for the generalized functions. The rule is described explicitly in the cases of K–k-Schur functions and k-Schur functions, with concrete descriptions and algorithms for coefficients. Our work recovers the result of Bandlow, Schilling, and Zabrocki for k-Schur functions, and explains it as a degeneration of the rule for K–k-Schur functions. In particular, many other special cases promise to be detailed in the future.
This video is part of the European Non-Associative Algebra Seminar series.
