A generalization of the Murnaghan-Nakayama rule for $K$-$k$-Schur and $k$-Schur functions

Abstract: 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 talk will be on Zoom only.

K-theory and homologyquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Paris algebra seminar

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