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Infinite Analysis Seminar Tokyo
Seminar information archive ～11/13｜Next seminar｜Future seminars 11/14～
| Date, time & place | Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
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Next seminar
2025/11/19
16:00-18:00 Room #156 (Graduate School of Math. Sci. Bldg.)
Hiroaki Karuo (Gakushuin)
Finite-dimensional irreducible representations of stated higher skein algebras and Fock--Goncharov algebras (JAPANESE)
Hiroaki Karuo (Gakushuin)
Finite-dimensional irreducible representations of stated higher skein algebras and Fock--Goncharov algebras (JAPANESE)
[ Abstract ]
The skein algebra is a quantum algebra defined from an oriented surface and $\mathfrak{sl}_2\mathbb{C}$. There is a
generalization with respect to $\mathfrak{sl}_n\mathbb{C}$, called the stated $\mathrm{SL}(n)$-skein algebra, related to higher Teich\"uller theory, which is compatible with splitting of a surface. To understand its algebraic structure, we would like to know finite-dimensional irreducible representations. Among its finite-dimensional irreducible representations, it is known that those with the highest dimension are one-to-one correspondence with the points of a subset of the maximal spectrum of its center. In this talk, I will start with basics of stated $\mathrm{SL}(n,\mathbb{C})$-skein algebras and explain how to use Fock--Goncharov algebras to understand the representations with the highest dimensions. This is a joint work with Zhihao Wang (KIAS).
The skein algebra is a quantum algebra defined from an oriented surface and $\mathfrak{sl}_2\mathbb{C}$. There is a
generalization with respect to $\mathfrak{sl}_n\mathbb{C}$, called the stated $\mathrm{SL}(n)$-skein algebra, related to higher Teich\"uller theory, which is compatible with splitting of a surface. To understand its algebraic structure, we would like to know finite-dimensional irreducible representations. Among its finite-dimensional irreducible representations, it is known that those with the highest dimension are one-to-one correspondence with the points of a subset of the maximal spectrum of its center. In this talk, I will start with basics of stated $\mathrm{SL}(n,\mathbb{C})$-skein algebras and explain how to use Fock--Goncharov algebras to understand the representations with the highest dimensions. This is a joint work with Zhihao Wang (KIAS).
