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Chebyshev Polynomials and Inequalities for Kleinian Groups
- Source :
- Communications in Contemporary Mathematics, (2021) 2150102, 22 pages
- Publication Year :
- 2021
-
Abstract
- The principal character of a representation of the free group of rank two into PSL(2, C) is a triple of complex numbers that determines an irreducible representation uniquely up to conjugacy. It is a central problem in the geometry of discrete groups and low dimensional topology to determine when such a triple represents a discrete group that is not virtually abelian, that is a Kleinian group. A classical necessary condition is J{\o}rgensen's inequality. Here we use certainly shifted Chebyshev polynomials and trace identities to determine new families of such inequalities, some of which are best possible. The use of these polynomials also shows how we can identify the principal character of some important subgroups from that of the group itself.<br />Comment: 18 pages
- Subjects :
- Mathematics - Complex Variables
Primary 30C60, 30F40, Secondary 20H10, 53A35
Subjects
Details
- Database :
- arXiv
- Journal :
- Communications in Contemporary Mathematics, (2021) 2150102, 22 pages
- Publication Type :
- Report
- Accession number :
- edsarx.2103.05696
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1142/S0219199721501029