-Deformations and -deformations of Markov triples
arXiv:2008.12913
Abstract
In this paper, we generalize the Markov triples in two different directions. One is generalization in direction of using the -deformation of rational number introduced by \cite{MO} in connection with cluster algebras, quantum topology and analytic number theory. The other is direction using castling transforms of prehomogeneous vector spaces \cite{SaKi} which plays an important role in the study of representation theory and automorphic function. In addition, the present paper gives a relationship between the two generalizations. This may provide some kind of bridging between different fields.