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Article overview
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A Lie-algebraic approach to the local index theorem on compact homogeneous spaces | Seunghun Hong
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22 Oct 2012 | Abstract: | Using a K-theory point of view, R. Bott related the Atiyah-Singer index
theorem for elliptic operators on compact homogeneous spaces to the Weyl
character formula. This dissertation explains how to prove the local index
theorem for compact homogenous spaces using Lie algebra methods. The method
follows in outline the proof of the local index theorem due to N. Berline and
M. Vergne. But the use of B. Kostant’s cubic Dirac operator in place of the
Riemannian Dirac operator leads to substantial simplifications. An important
role is also played by the quantum Weil algebra of A. Alekseev and E.
Meinrenken. | Source: | arXiv, 1210.5855 | Services: | Forum | Review | PDF | Favorites |
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