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arXiv · 1111.2749

Harish-Chandra's volume formula via Weyl's Law and Euler-Maclaurin formula

Seunghun Hong
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Abstract

Harish-Chandra's volume formula shows that the volume of a flag manifold $G/T$, where the measure is induced by an invariant inner product on the Lie algebra of $G$, is determined up to a scalar by the algebraic properties of $G$. This article explains how to deduce Harish-Chandra's formula from Weyl's law by utilizing the Euler-Maclaurin formula. This approach leads to a mystery that lies under the Atiyah-Singer index theorem.

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BibTeXRIS

Seunghun Hong. 2013-10-03. Harish-Chandra's volume formula via Weyl's Law and Euler-Maclaurin formula. https://doi.org/10.1016/j.difgeo.2014.11.006

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