Spectral Functions Of Hyperbolic Geometry Research Articles

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

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.

Vector generation functions, q-spectral functions of hyperbolic geometry, and vertex operators for quantum affine algebras

We investigate the concept of q-replicated argument in symmetric functions with its connection to spectral functions of hyperbolic geometry. This construction suffices for vector generation functions in the form of q-series and string theory. We hope that the mathematical side of the construction can be enriched by ideas coming from physics.

S-functions, spectral functions of hyperbolic geometry, and vertex operators with applications to structure for Weyl and orthogonal group invariants

In this paper we analyze the quantum homological invariants (the Poincaré polynomials of the slN link homology). In the case when the dimensions of homologies of appropriate topological spaces are precisely known, the procedure of the calculation of the Kovanov–Rozansky type homology, based on the Euler–Poincaré formula can be appreciably simplified. We express the formal character of the irreducible tensor representation of the classical groups in terms of the symmetric and spectral functions of hyperbolic geometry. On the basis of Labastida–Mariño–Ooguri–Vafa conjecture, we derive a representation of the Chern–Simons partition function in the form of an infinite product in terms of the Ruelle spectral functions (the cases of a knot, unknot, and links have been considered). We also derive an infinite-product formula for the orthogonal Chern–Simons partition functions and analyze the singularities and the symmetry properties of the infinite-product structures.

Generalized $$q$$ q -deformed correlation functions as spectral functions of hyperbolic geometry

We analyze the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite-dimensional Lie algebras, MacMahon and Ruelle functions. By definition p-dimensional MacMahon function, with \(p\le 3\), is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c = 1 CFT, and, as such, they can be generalized to \(p>3\). With some abuse of language we call the latter amplitudes generalized MacMahon functions. In this paper we show that generalized p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson–Selberg function of three-dimensional hyperbolic geometry.