Hilbert measures on orbit spaces of coregular Om-modules

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-03-10 DOI:10.1016/j.geomphys.2025.105473

Hans-Christian Herbig , Christopher W. Seaton , Lillian Whitesell

引用次数: 0

Abstract

We construct canonical measures, referred to as Hilbert measures, on orbit spaces of classical coregular representations of the orthogonal groups

O_{m}

. We observe that the measures have singularities along non-principal strata of the orbit space if and only if the number of copies of the defining representation of

O_{m}

is equal to m.

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核心垚模块轨道空间上的希尔伯特量纲

我们在正交群 Om 的经典核心格表示的轨道空间上构建了规范度量（称为希尔伯特度量）。我们发现，当且仅当 Om 的定义表示的份数等于 m 时，这些度量沿轨道空间的非主层具有奇点。

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

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity