2020/08/29 by Takeyoshi Kogiso, Kogiso, Takeyoshi · 1 citation
Mathematics · #11Axx 30Bxx 11Sxx #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2008.12913
openalex publication_date 2020/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citeMO in connection with cluster algebras, quantum topology and analytic number theory. The other is direction using castling transforms of prehomogeneous vector spaces \citeSaKi 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.