26 citations · 71 across the 21 of their papers we have counts for
24 papers
On the expansion formulas of cluster varieties from surfaces and their combinatorial properties
Vu Tung Lam Dinh, Ivan Chi-Ho Ip
This paper explores the cluster algebra structure of the moduli space of twisted -local systems on a surface. We der…
On the correspondence between perfect matchings and compatible pairs for affine cluster algebra
Ivan Ip, Duy Phan
We study cluster algebra of affine type by using two methods including counting the numbers of perfect matchings on snake graphs and compatible pairs on maximal Dyck pa…
On the polynomiality conjecture of cluster realization of quantum groups
Ivan Chi-Ho Ip, Jeff York Ye
In this paper, we give a sufficient and necessary condition for a regular element of a quantum cluster algebra to be universally polynomial. This resol…
Quantum cluster mutations and reduced word graphs
Ivan Chi-Ho Ip
We give an algebraic proof of the independence of Coxeter moves involved in the construction of positive representations of split-real quantum groups, thus completing a gap in the…
Positive Representations with Zero Casimirs
Ivan Chi-Ho Ip, Ryuichi Man
In this paper, we construct a new family of generalization of the positive representations of split-real quantum groups based on the degeneration of the Casimir operators acting as…
Parabolic Positive Representations of
Ivan Chi-Ho Ip
We construct a new family of irreducible representations of and its modular double by quantizing the classical parabolic induction correspo…