量子上同调中的仿射对称性:修正和新结果

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Research Letters Pub Date : 2023-01-01 DOI:10.4310/mrl.2023.v30.n2.a3

Pierre-Emmanuel Chaput, Nicolas Perrin

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引用次数: 0

摘要

在前一篇有理齐次空间的等变量子上同调的仿射对称性中，给出了任意齐次空间的量子上同调中一些特殊的Schubert类的乘法的一般公式。虽然这个公式在非等变情况下是正确的，但所陈述的等变情况是错误的。我们对等变公式进行了修正，从而给出了非等变公式的正确论证。我们还给出了仿射格拉斯曼的等变同调的新公式，这些公式可以推导出Pieri型公式。

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Affine symmetries in quantum cohomology: corrections and new results

In a previous paper Affine symmetries of the equivariant quantum cohomology of rational homogeneous spaces, a general formula was given for the multiplication by some special Schubert classes in the quantum cohomology of any homogeneous space. Although this formula is correct in the non equivariant setting, the stated equivariant version was wrong. We provide corrections for the equivariant formula, thus giving a correct argument for the non equivariant formula. We also give new formulas in the equivariant homology of the affine grassmannian that could lead to Pieri type formulas.

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来源期刊

Mathematical Research Letters 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6.0 months

期刊介绍： Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.