• Corpus ID: 250264602

Skein and cluster algebras of unpunctured surfaces for $\mathfrak{sp}_4$

@inproceedings{Ishibashi2022SkeinAC,
  title={Skein and cluster algebras of unpunctured surfaces for \$\mathfrak\{sp\}\_4\$},
  author={Tsukasa Ishibashi and Wataru Yuasa},
  year={2022}
}
Continuing to our previous work [IY21] on the sl3-case, we introduce a skein algebra S q sp 4 ,Σ consisting of sp4-webs on a marked surface Σ with certain “clasped” skein relations at special points, and investigate its cluster nature. We also introduce a natural Zq-form S Zq sp 4 ,Σ ⊂ S q sp 4 ,Σ, while the natural coefficient ring R of S q sp 4 ,Σ includes the inverse of the quantum integer [2]q. We prove that its boundary-localization S Zq sp 4 ,Σ[∂ ] is included into a quantum cluster… 

References

SHOWING 1-10 OF 24 REFERENCES

Quantum traces and embeddings of stated skein algebras into quantum tori

The stated skein algebra of a punctured bordered surface (or equivalently, a marked surface) is a generalization of the well-known Kauffman bracket skein algebra of unmarked surfaces and can be

SU(3)-skein algebras and webs on surfaces

The $$SU_3$$ S U 3 -skein algebra of a surface F is spanned by isotopy classes of certain framed graphs in $$F\times I$$ F × I called 3-webs subject to the skein relations encapsulating relations

Quantum geometry of moduli spaces of local systems and representation theory

Let G be a split semi-simple adjoint group, and S an oriented surface with punctures and special boundary points. We introduce a moduli space P(G,S) parametrizing G-local system on S with some

Moduli spaces of local systems and higher Teichmüller theory

Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S

Cluster realizations of Weyl groups and higher Teichmüller theory

For a symmetrizable Kac-Moody Lie algebra $\mathfrak{g}$, we construct a family of weighted quivers $Q_m(\mathfrak{g})$ ($m \geq 2$) whose cluster modular group $\Gamma_{Q_m(\mathfrak{g})}$ contains

Triangular decomposition of skein algebras

By introducing a finer version of the Kauffman bracket skein algebra, we show how to decompose the Kauffman bracket skein algebra of a surface into elementary blocks corresponding to the triangles in

Cluster algebras III: Upper bounds and double Bruhat cells

We continue the study of cluster algebras initiated in math.RT/0104151 and math.RA/0208229. We develop a new approach based on the notion of an upper cluster algebra, defined as an intersection of

The quantum G_2 link invariant

We derive an inductive, combinatorial definition of a polynomial-valued regular isotopy invariant of links and tangled graphs. We show that the invariant equals the Reshetikhin-Turaev invariant