Cylindric skew Schur functions
Cylindric skew Schur functions
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圆柱斜 Schur 函数
DOI：
10.1016/j.aim.2005.07.011
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发表时间：
2004
影响因子：
1.7
通讯作者：
Peter R. W. McNamara
中科院分区：
文献类型：
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作者：
Peter R. W. McNamara
斜Schur函数是斜Schur函数的推广，在P-划分的研究中自然出现。此外，A. Postnikov表明，他们有一个很强的连接与一个相当大的当前利益的问题：即找到一个组合证明的非负的3点Gromov-Witten不变量。在解释了这些动机之后，我们从Schur正性的角度研究了圆柱斜Schur函数。利用I. Gessel和C. Krattenthaler，我们推广了A.伯特伦岛Ciocan-Fontanine和W.富尔顿，从而给出了任意圆柱形斜Schur函数的斜Schur函数展开式.虽然我们表明，没有非平凡的圆柱斜舒尔功能是舒尔积极的，我们猜想，这可以调和使用新概念的圆柱舒尔积极性。
Cylindric skew Schur functions, which are a generalisation of skew Schur functions, arise naturally in the study of P-partitions. Also, recent work of A. Postnikov shows they have a strong connection with a problem of considerable current interest: that of finding a combinatorial proof of the non-negativity of the 3-point Gromov–Witten invariants. After explaining these motivations, we study cylindric skew Schur functions from the point of view of Schur-positivity. Using a result of I. Gessel and C. Krattenthaler, we generalise a formula of A. Bertram, I. Ciocan-Fontanine and W. Fulton, thus giving an expansion of an arbitrary cylindric skew Schur function in terms of skew Schur functions. While we show that no non-trivial cylindric skew Schur functions are Schur-positive, we conjecture that this can be reconciled using the new concept of cylindric Schur-positivity.