q-Deformations and t-deformations of Markov triples
Abstract
In this paper, we generalize the Markov triples in two different directions. One is generalization in direction of using the q-deformation of rational number introduced by MO in connection with cluster algebras, quantum topology and analytic number theory. The other is direction using castling transforms of prehomogeneous vector spaces 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.
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