The $\ast$-Markov equation for Laurent polynomials

Abstract

We consider the $\ast$-Markov equation for the symmetric Laurent polynomials in three variables with integer coefficients, which is an equivariant analog of the classical Markov equation for integers. We study how the properties of the Markov equation and its solutions are reflected in the properties of the $\ast$-Markov equation and its solutions.

68 pages, 11 figures; corrected typos, added references; v4: Introduction extended, references added