加泰罗尼亚函数和𝑘-Schur阳性

IF 3.5 1区数学 Q1 MATHEMATICS Journal of the American Mathematical Society Pub Date : 2018-04-10 DOI:10.1090/JAMS/921

J. Blasiak, J. Morse, Anna Y. Pun, D. Summers

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引用次数: 12

摘要

证明了分次k-舒尔函数是旗变上向量丛的G-等变Euler特征，解决了陈海曼的一个猜想。我们揭示了分次k k-Schur函数的一个新的奇迹移位不变性，并通过使用强标记表提供直接组合公式，以尽可能强的项解决了Schur正性和k k-分支猜想。

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Catalan functions and 𝑘-Schur positivity

We prove that graded k k -Schur functions are G G -equivariant Euler characteristics of vector bundles on the flag variety, settling a conjecture of Chen-Haiman. We expose a new miraculous shift invariance property of the graded k k -Schur functions and resolve the Schur positivity and k k -branching conjectures in the strongest possible terms by providing direct combinatorial formulas using strong marked tableaux.

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来源期刊

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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