自旋模中乘法的矩阵公式

Q3 Mathematics

Communications in Mathematics Pub Date : 2023-04-04 DOI:10.46298/cm.11156

Lucas Fresse, S. Mehdi

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引用次数: 0

摘要

我们得到了复半单李代数中Levi子代数Clifford代数的自旋模的权重的乘积的归纳和枚举公式。我们的公式只涉及矩阵和表，我们的技术结合了线性代数、李理论和组合数学。此外，这表明了与复杂幂零轨道的关系。重点讨论了特殊线性李代数$\mathfrak｛sl｝（n，｛\mathbbC｝）$的情形。

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Matrix formulas for multiplicities in the spin module

We obtain inductive and enumerative formulas for the multiplicities of the weights of the spin module for the Clifford algebra of a Levi subalgebra in a complex semisimple Lie algebra. Our formulas involve only matrices and tableaux, and our techniques combine linear algebra, Lie theory, and combinatorics. Moreover, this suggests a relationship with complex nilpotent orbits. The case of the special linear Lie algebra $\mathfrak{sl}(n,{\mathbb C})$ is emphasized.

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来源期刊

Communications in Mathematics Mathematics-Mathematics (all)

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

45 weeks

期刊介绍： Communications in Mathematics publishes research and survey papers in all areas of pure and applied mathematics. To be acceptable for publication, the paper must be significant, original and correct. High quality review papers of interest to a wide range of scientists in mathematics and its applications are equally welcome.