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

详细信息    查看全文

• 作者：A.A. Bytsenko^a ; ^{aabyts@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; M. Chaichian^b ; ^{masud.chaichian@helsinki.fi" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Nuclear Physics B
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：907
• 期：Complete
• 页码：258-285
• 全文大小：486 K

文摘

In this paper we analyze the quantum homological invariants (the Poincaré polynomials of the sl_N${\mathfrak{sl}}_N$ 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–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.