Harish-Chandra's volume formula via Weyl's Law and Euler-Maclaurin formula
Representation Theory
2016-04-12 v2 Differential Geometry
Abstract
Harish-Chandra's volume formula shows that the volume of a flag manifold , where the measure is induced by an invariant inner product on the Lie algebra of , is determined up to a scalar by the algebraic properties of . 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.
Keywords
Cite
@article{arxiv.1111.2749,
title = {Harish-Chandra's volume formula via Weyl's Law and Euler-Maclaurin formula},
author = {Seunghun Hong},
journal= {arXiv preprint arXiv:1111.2749},
year = {2016}
}