State-clasp correspondence for skein algebras

Abstract: We introduce the stated and the clasped sp_4-skein algebras for an oriented surface with marked points on the boundary. Moreover, we show that the reduced version of the stated g-skein algebra is isomorphic to the boundary-localization of the clasped g-skein algebra for g=sl_2, sl_3, or sp_4. This isomorphism is a quantum counterpart of the two descriptions of the cluster algebra of the surface associated with g in terms of the matrix coefficients of Wilson lines and cluster variables, respectively. This talk is based on a joint work with Tsukasa Ishibashi (Tohoku Univ.).

mathematical physicsalgebraic geometrygeometric topologyquantum algebra

Audience: researchers in the discipline

Geometry, Algebra and Physics at KIAS