论文标题
轨道积分和量度正常化
Orbital integrals and normalizations of measures
论文作者
论文摘要
本说明提供了一个非正式的介绍，并提供了示例的一些技术方面，这些方面是在Langlands，Frenkel-Langlands-Ngô和Altug of Beyond Endoscopy of Beyond Endoscopy of Langlands，Frenkel-Langlands-ngô和Altug进行的轨道积分措施的一些技术方面。特别是，我们调查了关于代数托里的不同相关措施，并解释了与塔玛川数字的联系。我们完整地详细介绍了$ \ mathrm {gl} _2 $的示例。马修·科斯特（Matthew Koster）的附录说明了谎言代数$ \ mathfrak {sl} _2 $和$ \ mathfrak {so} _3 $，这是Orbits上所谓的几何测度与Kirillov措施上的几何几何措施之间的关系，而Kirillov措施在linearear dualge alge alge alge alge alge Algebra中的联合结成轨道上的措施。
This note provides an informal introduction, with examples, to some technical aspects of the re-normalization of measures on orbital integrals used in the work of Langlands, Frenkel-Langlands-Ngô, and Altug on Beyond Endoscopy. In particular, we survey different relevant measures on algebraic tori and explain the connection with the Tamagawa numbers. We work out the example of $\mathrm{GL}_2$ in complete detail. The Appendix by Matthew Koster illustrates, for the Lie algebras $\mathfrak{sl}_2$ and $\mathfrak{so}_3$, the relation between the so-called geometric measure on the orbits and Kirillov's measure on co-adjoint orbits in the linear dual of the Lie algebra.
