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arXiv · 2012.12662

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

A. A. Bytsenko·M. Chaichian·A. E. Gonçalves
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Abstract

In this article we exploit Ruelle-type spectral functions and analyze the Verma module over Virasoro algebra, boson-fermion correspondence, the analytic torsion, the Chern-Simons and $\eta$ invariants, as well as the generation function associated to dimensions of the Hochschild homology of the crossed product $\mathbb{C}[S_n]\ltimes \mathcal{A}^{\otimes n}$ ($\mathcal{A}$ is the $q$-Weyl algebra). After analysing the Chern-Simons and $\eta$ invariants of Dirac operators by using irreducible $SU(n)$-flat connections on locally symmetric manifolds of non-positive section curvature, we describe the exponential action for the Chern-Simons theory.

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A. A. Bytsenko, M. Chaichian, A. E. Gonçalves. 2020-11-18. Hilbert schemes, Verma modules and spectral functions of hyperbolic geometry with application to quantum invariants. https://doi.org/10.1142/s0217751x19300060

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