arXiv subjects

Tyakal N. Venkataramana

Publications and source records attributed to Tyakal N. Venkataramana.

6 recordsLinked to original sources

arXiv2022

Unipotent Generators for Arithmetic Groups

We sketch a simplification of proofs of old results on the arithmeticity of the group generated by opposing integral unipotent radicals in higher rank arithmetic groups

math.GR↗

arXiv2021

Centrality of the congruence subgroup kernel of higher rank non-uniform arithmetic groups

We give here a simple proof of the centrality of the congruence subgroup kernel in the higher rank isotropic case.

math.NT↗

arXiv2019

Differential Equations and Monodromy

In these expository notes, we describe results of Cauchy, Fuchs and Pochhammer on differential equations. We then apply these results to hypergeometric differential equation of type $_nF_{n-1}$ and describe Levelt's theorem determining the monodromy representation explicitly in terms of the hypergeometric equation. We also give a brief overview, without proofs, of results of Beukers and Heckman, on the Zariski closure of the monodromy group of the hypergeometric equation. In the last section, we recall some recent results on thin-ness and arithmeticity of hypergeometric monodromy groups.

math.CA↗

arXiv2013

Image of the Burau Representation at $d$-th Roots of unity

We prove that the image of the Full braid group $B_{n+1}$ on $n+1$ strands under the Burau representation, evaluated at a primitive $d$-th root of unity is arithmetic provided $n\geq d$.

math.GR↗

arXiv2013

Monodromy of Cyclic Coverings of the Projective Line

We show that the image of the pure braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of branch points is sufficiently large compared to the degree.

math.GR↗

arXiv2013

Arithmeticity of Certain Symplectic Hypergeometric Groups

We give a sufficient condition on a pair of (primitive) integral polynomials that the associated hypergeometric group (monodromy group of the corresponding hypergeometric differential equation) is an arithmetic subgroup of the integral symplectic group.

math.GR↗