Kirillov Polynomials for the Exceptional Lie Algebra $\mathfrak g_{2}$

Q3 Mathematics

Arnold Mathematical Journal Pub Date : 2024-04-04 DOI:10.1007/s40598-024-00247-8

Martin T. Luu

引用次数: 0

Abstract

As part of the development of the orbit method, Kirillov has counted the number of strictly upper triangular matrices with coefficients in a finite field of q elements and fixed Jordan type. One obtains polynomials with respect to q with many interesting properties and close relation to type A representation theory. In the present work, we develop the corresponding theory for the exceptional Lie algebra $\mathfrak g_2$. In particular, we show that the leading coefficient can be expressed in terms of the Springer correspondence.

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特殊列代数 $$\mathfrak g_{2}$ 的基里洛夫多项式

作为轨道方法发展的一部分，基里洛夫计算了在具有 q 个元素和固定约旦类型的有限域中具有系数的严格上三角矩阵的数量。我们得到了关于 q 的多项式，它们具有许多有趣的性质，并与 A 型表示理论密切相关。在本研究中，我们发展了例外李代数（\mathfrak g_2\）的相应理论。我们特别指出，前导系数可以用 Springer 对应关系来表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Arnold Mathematical Journal Mathematics-Mathematics (all)

CiteScore

1.50

自引率

0.00%

发文量

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Kirillov Polynomials for the Exceptional Lie Algebra \(\mathfrak g_{2}\)

Abstract