20 citations · 102 across the 15 of their papers we have counts for
15 papers
Algebraic study of quantum configuration spaces of decorated flags
Tsukasa Ishibashi, Hironori Oya
Let be a connected, simply connected complex simple algebraic group and its base affine space, whose elements are called decorated flags. We introduce the…
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…
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…
Isomorphisms among quantum Grothendieck rings and cluster algebras
Ryo Fujita, David Hernandez, Se-jin Oh +1
We establish a cluster theoretical interpretation of the isomorphisms of [F.-H.-O.-O., J. Reine Angew. Math., 2022] among quantum Grothendieck rings of representations of quantum l…
for cluster algebras from moduli spaces of -local systems
Tsukasa Ishibashi, Hironori Oya, Linhui Shen
For a finite-dimensional simple Lie algebra admitting a non-trivial minuscule representation and a connected marked surface with at least two marked points and n…
Isomorphisms among quantum Grothendieck rings and propagation of positivity
Ryo Fujita, David Hernandez, Se-jin Oh +1
Let ( be a pair of complex finite-dimensional simple Lie algebras whose Dynkin diagrams are related by (un)folding, with being of simply-lace…
Wilson lines and their Laurent positivity
Tsukasa Ishibashi, Hironori Oya
For a marked surface and a semisimple algebraic group of adjoint type, we study the Wilson line morphism associated with the homotopy clas…
Newton-Okounkov polytopes of Schubert varieties arising from cluster structures
Naoki Fujita, Hironori Oya
The theory of Newton-Okounkov bodies is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of pr…
Cluster realizations of Weyl groups and higher Teichmüller theory
Rei Inoue, Tsukasa Ishibashi, Hironori Oya
For a symmetrizable Kac-Moody Lie algebra , we construct a family of weighted quivers () whose cluster modular group $Γ_{Q_m(\mathfrak{g…
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…
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…
A comparison of Newton-Okounkov polytopes of Schubert varieties
Naoki Fujita, Hironori Oya
A Newton-Okounkov body is a convex body constructed from a polarized variety with a valuation on its function field. Kaveh (resp., the first author and Naito) proved that the Newto…
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…