130 citations · 1k across the 44 of their papers we have counts for
44 papers
Torus links and -log VOA
Kazuhiro Hikami, Shoma Sugimoto
We reveal an intimate connection between the torus link and the logarithmic VOA. We show that the singlet character of -log VOA at the root of unity coin…
Non-semisimple invariants and Habiro's series
Anna Beliakova, Kazuhiro Hikami
In this paper we establish an explicit relationship between Habiro's cyclotomic expansion of the colored Jones polynomial (evaluated at a p-th root of unity) and the Akutsu-Deguchi…
DAHA and skein algebra on surface: double-torus knots
Kazuhiro Hikami
We study a topological aspect of rank-1 double affine Hecke algebra (DAHA). Clarified is a relationship between the DAHA of A1-type (resp. CC1-type) and the skein algebra on a once…
Note on character varieties and cluster algebras
Kazuhiro Hikami
We use Bonahon-Wong's trace map to study character varieties of the once-punctured torus and of the 4-punctured sphere. We clarify a relationship with cluster algebra associated wi…
Torus knots and quantum modular forms
Kazuhiro Hikami, Jeremy Lovejoy
In this paper we compute a -hypergeometric expression for the cyclotomic expansion of the colored Jones polynomial for the left-handed torus knot and use this to defi…
Braiding Operator via Quantum Cluster Algebra
Kazuhiro Hikami, Rei Inoue
We construct a braiding operator in terms of the quantum dilogarithm function based on the quantum cluster algebra. We show that it is a q-deformation of the R-operator for which h…