Fricke identities, Frobenius k-characters and Markov equation

2019/12/18 by Buchstaber, V. M., Veselov, A. P.
#01A55 #20C05 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1912.08705

Abstract

In 1896 Frobenius and Fricke had published two seemingly unrelated papers: Frobenius had started to develop his theory of k-characters for finite groups motivated by Dedekind's question about factorisation of the group determinant, while Fricke followed Klein's approach to the uniformization theorem. We show that in fact these two works can be naturally linked and both are related to remarkable Markov's paper of 1880 on arithmetic of binary quadratic forms.

Related

• Two- & Three-character solutions to MLDEs and Ramanujan-Eisenstein Identities for Fricke Groups
• Generalization of Frobenius' theorem for group determinants
• On polynomial representations of finite groups
• Recherches autour de la theorie de Markoff
• On the Markov numbers: fixed numerator, denominator, and sum conjectures