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

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Bytsenko , A A & Chaichian , M 2016 , ' S-functions, spectral functions of hyperbolic geometry, and vertex operators with applications to structure for Weyl and orthogonal group invariants ' , Nuclear Physics, Section B , vol. 907 , pp. 258-285 . https://doi.org/10.1016/j.nuclphysb.2016.03.029

Title: S-functions, spectral functions of hyperbolic geometry, and vertex operators with applications to structure for Weyl and orthogonal group invariants
Author: Bytsenko, A. A.; Chaichian, M.
Contributor: University of Helsinki, Department of Physics
Date: 2016-06
Language: eng
Number of pages: 28
Belongs to series: Nuclear Physics, Section B
ISSN: 0550-3213
URI: http://hdl.handle.net/10138/184733
Abstract: In this paper we analyze the quantum homological invariants (the Poincare polynomials of the sI(N) 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-Poincare 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-Marino-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 Chem-Simons partition functions and analyze the singularities and the symmetry properties of the infinite-product structures. (C) 2016 The Authors. Published by Elsevier B.V.
Subject: QUANTUM GROUP INVARIANTS
SYMMETRICAL FUNCTIONS
TOPOLOGICAL STRINGS
MATRIX FACTORIZATIONS
LINK POLYNOMIALS
GROUP CHARACTERS
KNOT INVARIANTS
LARGE N
REPRESENTATIONS
ALGEBRAS
114 Physical sciences
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