The purpose of this chapter is to establish Theorem 6.1.1. The proof consists in making *b* → +∞ in equation (4.6.1), that is, we evaluate the limit as *b* → +∞ of

This chapter is organized as follows. In section 9.1, we state various estimates on the hypoelliptic heat kernels, which are valid for *b* ≥ 1. The proofs of these estimates are deferred to chapter 15. They will be used for dominated convergence in the hypoelliptic orbital integrals as *b* → +∞.

In section 9.2, we make a natural rescaling on the coordinates parametrizing .

In section 9.3, we introduce a conjugation on the Clifford variables, which is ...

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