Hilbert schemes, Verma modules and spectral functions of hyperbolic geometry with application to quantum invariants

Abstract

In this paper we exploit Ruelle-type spectral functions and analyze the Verma module over Virasoro algebra, boson–fermion correspondence, the analytic torsion, the Chern–Simons and [Formula: see text] invariants, as well as the generating function associated to dimensions of the Hochschild homology of the crossed product [Formula: see text] ([Formula: see text] is the [Formula: see text]-Weyl algebra). After analyzing the Chern–Simons and [Formula: see text] invariants of Dirac operators by using irreducible [Formula: see text]-flat connections on locally symmetric manifolds of nonpositive section curvature, we describe the exponential action for the Chern–Simons theory.