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pro vyhledávání: '"Yuasa, Wataru"'
We propose a skein model for the quantum cluster algebras of surface type with coefficients. We introduce a skein algebra $\mathscr{S}_{\Sigma,\mathbb{W}}^{A}$ of a walled surface $(\Sigma,\mathbb{W})$, and prove that it has a quantum cluster structu
Externí odkaz:
http://arxiv.org/abs/2312.02861
Autor:
Ishibashi, Tsukasa, Yuasa, Wataru
Continuing to our previous work [IY21](arXiv:2101.00643) on the $\mathfrak{sl}_3$-case, we introduce a skein algebra $\mathscr{S}_{\mathfrak{sp}_4,\Sigma}^{q}$ consisting of $\mathfrak{sp}_4$-webs on a marked surface $\Sigma$ with certain "clasped" s
Externí odkaz:
http://arxiv.org/abs/2207.01540
Autor:
Ishibashi, Tsukasa, Yuasa, Wataru
Publikováno v:
Math. Z. 303, 72 (2023)
For an unpunctured marked surface $\Sigma$, we consider a skein algebra $\mathscr{S}_{\mathfrak{sl}_{3},\Sigma}^{q}$ consisting of $\mathfrak{sl}_3$-webs on $\Sigma$ with the boundary skein relations at marked points. We construct a quantum cluster a
Externí odkaz:
http://arxiv.org/abs/2101.00643
Autor:
Yuasa, Wataru
The stability of coefficients of colored ($\mathfrak{sl}_2$-) Jones polynomials $\{J_{K,n}^{\mathfrak{sl}_2}(q)\}_n$ was discovered by Dasbach and Lin. This stability is now called the zero-stability of $J_{K,n}^{\mathfrak{sl}_2}(q)$. Armond showed z
Externí odkaz:
http://arxiv.org/abs/2007.15621
Autor:
Yuasa, Wataru
The $\mathfrak{sl}_3$ colored Jones polynomial $J_{\lambda}^{\mathfrak{sl}_3}(L)$ is obtained by coloring the link components with two-row Young diagram $\lambda$. Although it is difficult to compute $J_{\lambda}^{\mathfrak{sl}_3}(L)$ in general, we
Externí odkaz:
http://arxiv.org/abs/2003.12278
Autor:
Yuasa, Wataru
We show that the $A_2$ clasps in the Karoubi envelope of $A_2$ spider satisfy the recursive formula of the two-variable Chebyshev polynomials of the second kind associated with a root system of type $A_2$. The $A_2$ spider is a diagrammatic descripti
Externí odkaz:
http://arxiv.org/abs/1903.01099
Autor:
Yuasa, Wataru
This paper contains two topics, the index of a power subgroup in the mapping class group $\mathcal{M}(0,2n)$ of a $2n$-punctured sphere and in the hyperelliptic mapping class group $\Delta(g,0)$ of an oriented closed surface of genus $g$. The main to
Externí odkaz:
http://arxiv.org/abs/1801.06026
Autor:
Yuasa, Wataru
We define a family of representations $\{\rho_n\}_{n\geq 0}$ of a pure braid group $P_{2k}$. These representations are obtained from an action of $P_{2k}$ on a certain type of $A_2$ web space with color $n$. The $A_2$ web space is a generalization of
Externí odkaz:
http://arxiv.org/abs/1711.05931
Autor:
Yuasa, Wataru
Publikováno v:
New York J. Math. (2018), vol. 24, 355--374
The Kauffman-Vogel polynomials are three variable polynomial invariants of $4$-valent rigid vertex graphs. A one-variable specialization of the Kauffman-Vogel polynomials for unoriented $4$-valent rigid vertex graphs was given by using the Kauffman b
Externí odkaz:
http://arxiv.org/abs/1708.09131
Autor:
Yuasa, Wataru
Publikováno v:
Proc. Amer. Math. Soc. (2018) vol. 146, no. 7, 355--374
The colored Jones polynomial is a $q$-polynomial invariant of links colored by irreducible representations of a simple Lie algebra. A $q$-series called a tail is obtained as the limit of the $\mathfrak{sl}_2$ colored Jones polynomials $\{J_n(K;q)\}_n
Externí odkaz:
http://arxiv.org/abs/1612.02144