论文标题
Murnaghan-Nakayama规则的概括$ k $ - $ k $ -schur和$ k $ -schur函数
A generalization of the Murnaghan-Nakayama rule for $K$-$k$-Schur and $k$-Schur functions
论文作者
论文摘要
$ k $ - $ k $ -schur函数和$ k $ -schur功能出现在$ k $ - 理论和仿射舒伯特·彩石作为舒伯特类的多项式代表中。在本文中，我们介绍了一个新的对称函数系列$ \ MATHCAL {F}_λ^{（K）} $，该家族通过$ K $ -K $ -K $ -SCHUR函数的Pieri规则和$ K $ -SCHUR函数来概括构造。然后，我们获得了广义功能的Murnaghan-Nakayama规则。在$ k $ - $ k $ -schur函数和$ k $ -schur函数的情况下，该规则明确描述了，具有具体的描述和系数算法。我们的工作恢复了Bandlow，Schilling和Zabrocki的结果，以$ K $ -SCHUR功能，并将其解释为$ K $ -K $ -K $ -SCHUR函数的规则退化。特别是，许多其他特殊情况和联系有望将来详细介绍。
The $K$-$k$-Schur functions and $k$-Schur functions appeared in the study of $K$-theoretic and affine Schubert Calculus as polynomial representatives of Schubert classes. In this paper, we introduce a new family of symmetric functions $\mathcal{F}_λ^{(k)}$, that generalizes the constructions via the Pieri rule of $K$-$k$-Schur functions and $ k$-Schur functions. 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 and connections promise to be detailed in the future.
