THE LAPLACIAN ON p-FORMS ON THE HEISENBERG GROUP
نویسنده
چکیده
The Novikov-Shubin invariants for a non-compact Riemannian manifold M can be defined in terms of the large time decay of the heat operator of the Laplacian on L p-forms, △p, on M . For the (2n + 1)-dimensional Heisenberg group H2n+1, the Laplacian △p can be decomposed into operators△p,n(k) in unitary representations β̄k which, when restricted to the centre of H, are characters (mapping ω to exp(−ikω)). The representation space is an anti-Fock space (F n ), of anti-holomorphic functions F on Cn such that ∫ Cn |F (z̄)|2e−1/4k|z| 2 dz < +∞. In this paper, the eigenvalues of △p,n(k) are calculated, for all n and p, using operators which commute with the Laplacian; this information determines the pth Novikov-Shubin invariant of H2n+1. Further, some eigenvalues of operators connected with nilpotent Lie groups of Heisenberg type are calculated in the later sections.
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