3 papers
math.QA2026
Integral cluster structures on quantized coordinate rings
Hironori Oya, Fan Qin, Milen Yakimov
We develop (quantum) cluster algebra structures over arbitrary commutative unital rings and prove that the (quantized) coordinate rings of connected simply-connected comple…
math.RT2025
A note on a cluster structure of the coordinate ring of a simple algebraic group
Hironori Oya
We show that the coordinate ring of a simply-connected simple algebraic group over the complex number field coincides with the Berenstein--Fomin--Zelevinsky cluster algebra and…
math.RT2018
Quantum Grothendieck ring isomorphisms, cluster algebras and Kazhdan-Lusztig algorithm
David Hernandez, Hironori Oya
We establish ring isomorphisms between quantum Grothendieck rings of certain remarkable monoidal categories of finite-dimensional representations of quantum affine algebras of type…