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Hypoelliptic Laplacian and Orbital Integrals (AM-177) by Jean-Michel Bismut

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Chapter Two

The hypoelliptic Laplacian on X = G/K

The purpose of this chapter is to construct the hypoelliptic Laplacian image, b > 0 acting on the total space of a vector bundle image over X = G/K. The operator image will be obtained using general constructions involving Clifford algebras and Heisenberg algebras, and also the Dirac operator of Kostant [Ko97].

This chapter is organized as follows. In section 2.1, we introduce a pair (G, K), the symmetric space

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