E7(7) 的狄拉克级数

IF 0.8 2区数学 Q2 MATHEMATICS

Israel Journal of Mathematics Pub Date : 2024-09-03 DOI:10.1007/s11856-024-2658-1

Yi-Hao Ding, Chao-Ping Dong, Lin Wei

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引用次数: 0

摘要

本文对 E7(7) 的所有狄拉克数列（即具有非零狄拉克同调的不可还原单元表示）进行了分类。其中一个关键因素是增强了 1969 年对 E7(7) 群的 Helgason-Johnson 约束。我们的计算部分支持了沃根的基本平行四边形（FPP）猜想。作为应用，当传递到狄拉克指数时，我们继续发现狄拉克同调的偶数部分和奇数部分之间的抵消。此外，我们首次发现了自旋最低 K 型具有乘数的狄拉克级数。

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Dirac series of E7(7)

This paper classifies all the Dirac series (that is, irreducible unitary representations having non-zero Dirac cohomology) of E₇₍₇₎. Enhancing the Helgason–Johnson bound in 1969 for the group E₇₍₇₎ is one key ingredient. Our calculation partially supports Vogan’s fundamental parallelepiped (FPP) conjecture. As applications, when passing to Dirac index, we continue to find cancellation between the even part and the odd part of Dirac cohomology. Moreover, for the first time, we find Dirac series whose spin lowest K-types have multiplicities.

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来源期刊

Israel Journal of Mathematics 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.