20 citations · 102 across the 15 of their papers we have counts for
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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…
The Chamber Ansatz for quantum unipotent cells
Hironori Oya
In this paper, we prove quantum analogues of the Chamber Ansatz formulae for unipotent cells. These formulae imply that the quantum twist automorphisms, constructed by Kimura and t…
Twist automorphisms on quantum unipotent cells and dual canonical bases
Yoshiyuki Kimura, Hironori Oya
In this paper, we construct twist automorphisms on quantum unipotent cells, which are quantum analogues of the Berenstein-Fomin-Zelevinsky twist automorphisms on unipotent cells. W…
Quantum twist maps and dual canonical bases
Yoshiyuki Kimura, Hironori Oya
In this paper, we show that quantum twist maps, introduced by Lenagan-Yakimov, induce bijections between dual canonical bases of quantum nilpotent subalgebras. As a corollary, we s…
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases
Hironori Oya
Let be a connected simply-connected simple complex algebraic group and the corresponding simple Lie algebra. In the first half of the present paper, we study the…