12 citations · 44 across the 21 of their papers we have counts for
22 papers
Index for a mutation loop
Tsukasa Ishibashi, Yuji Terashima
Motivated by the 3d-3d correspondence, we introduce an index for a mutation loop of a quiver and an integer . We prove its integrality $\mathcal{I}_…
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…
Fixed point theorem for cluster modular groups
Tsukasa Ishibashi
We prove that any finite subgroup of the cluster modular group has fixed points in the cluster manifolds $\mathcal{A}_{\boldsymbol{s}}(\mathbb{R}_{>0…
Adjoint Reidemeister torsion of 3-manifolds with torus boundary for semisimple algebraic groups
Tsukasa Ishibashi, Yuma Mizuno
Let be a compact oriented -manifold with boundary consisting of tori, and let be a semisimple algebraic group. We define the adjoint torsion function on the moduli stack…
Bounded -laminations and their intersection coordinates
Tsukasa Ishibashi, Zhe Sun, Wataru Yuasa
We introduce rational bounded -laminations on a marked surface as a proposed topological model for the rational tropical points $\mathcal{A}_{Sp_4,\…
Unbounded -laminations around punctures
Tsukasa Ishibashi, Shunsuke Kano
We continue to study the unbounded -laminations [IK22], with a focus on their structures at punctures. A key ingredient is their relation to the root data of $\mat…
Entropy of cluster DT transformations and the finite-tame-wild trichotomy of acyclic quivers
Tsukasa Ishibashi, Shunsuke Kano
The cluster algebra associated with an acyclic quiver has a special mutation loop , called the cluster Donaldson--Thomas (DT) transformation, related to the Auslander--Reiten tr…
Skein and cluster algebras with coefficients for unpunctured surfaces
Tsukasa Ishibashi, Shunsuke Kano, Wataru Yuasa
We propose a skein model for the quantum cluster algebras of surface type with coefficients. We introduce a skein algebra of a walled surface $(Σ,\…
Quantum duality maps, skein algebras and their ensemble compatibility
Tsukasa Ishibashi, Hiroaki Karuo
We generalize the quantum duality map of Allegretti--Kim [AK17] for punctured closed surfaces to general marked surfaces. When the marked surface has no…
Teichmüller and lamination spaces with pinnings
Tsukasa Ishibashi
We describe the spaces of the positive and tropical points of the moduli space introduced by Goncharov--Shen [GS19] as certain Teichmüller and lamination sp…
Skein and cluster algebras of unpunctured surfaces for
Tsukasa Ishibashi, Wataru Yuasa
Continuing to our previous work [IY21](arXiv:2101.00643) on the -case, we introduce a skein algebra consisting of $\mathfrak{…
Earthquake theorem for cluster algebras of finite type
Takeru Asaka, Tsukasa Ishibashi, Shunsuke Kano
We introduce a cluster algebraic generalization of Thurston's earthquake map for the cluster algebras of finite type, which we call the \emph{cluster earthquake map}. It is defined…
Unbounded -laminations and their shear coordinates
Tsukasa Ishibashi, Shunsuke Kano
Generalizing the work of Fock--Goncharov on rational unbounded laminations, we give a geometric model of the tropical points of the cluster variety $\mathcal{X}_{\mathfrak{sl}_3,Σ}…
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…
Skein and cluster algebras of unpunctured surfaces for
Tsukasa Ishibashi, Wataru Yuasa
For an unpunctured marked surface , we consider a skein algebra consisting of -webs on with the boundary skein relat…
Sign stability of mapping classes on marked surfaces II: general case via reductions
Tsukasa Ishibashi, Shunsuke Kano
We give a cluster algebraic description of the reduction procedure of mapping classes along a multicurve. Based on this description, we characterize pseudo-Anosov mapping classes o…
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…
A characterization of pseudo-Anosov mapping classes via tropical cluster transformations
Tsukasa Ishibashi, Shunsuke Kano
We give a characterization of generic pseudo-Anosov mapping classes purely in terms of their expressions in the shear coordinates, thus giving an answer to a problem raised by Papa…
Algebraic entropy of sign-stable mutation loops
Tsukasa Ishibashi, Shunsuke Kano
We introduce a property of mutation loops, called the sign stability, with a focus on an asymptotic behavior of the iteration of the tropical -transformation. A sign-s…
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…
Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists
Tsukasa Ishibashi
We give a method to compute presentations of saturated cluster modular groups. Using this, we obtain finite presentations of the saturated cluster modular groups of finite mutation…
On a Nielsen-Thurston classification theory for cluster modular groups
Tsukasa Ishibashi
We classify elements of a cluster modular group into three types. We characterize them in terms of fixed point property of the action on the tropical compactifications associated w…