Representations of the quantum groups at roots of unity and its application to knot theory

统一根处量子群的表示及其在纽结理论中的应用

• 批准号: 22540236
• 负责人: MURAKAMI Jun
• 金额: $ 2.58万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540236/
• 关键词: 可積分系; 量子群; 量子不変量; 位相幾何学; 作用素環; 結び目理論; 双曲幾何学; ３次元多様体; 多面体; 結び目; 射影加群; 双曲構造; 体積

We did research rerated to the ‘Volume Conjecture’ which gives a relation between the quantum invariant related to the quantum group Uq(sl2), and, by noticing the non-semisimple representation of it, such representations and the related knot invariants were studied. By applying the volume conjecture, the geometric structure of a knot complement and the volumes of polyhedrons in a three space with a constant curvature were studied. Moreover, new invariants of knots in a three manifolds were constructed from the non-semisimple representations.

我们研究了给出与量子群Uq(SL2)有关的量子不变量之间关系的“体积猜想”，并注意到它的非半简单表示，研究了这种表示和相关的纽结不变量。利用体积猜想，研究了常曲率空间中结点补的几何结构和多面体的体积。此外，从非半单表示出发，构造了三个流形中纽结的新不变量。

项目成果

Volume of a doubly truncated hyperbolic tetra- hedron

双截双曲四面体的体积

• DOI: 10.1007/s00010-012-0153-y
• 发表时间: 2012
• 期刊: Aequat. Math
• 作者: Kolpakov;Alexander ; Murakami,Jun
• 通讯作者: Alexander ; Murakami,Jun

The complex volumes of twist knots via colored Jones polynomials

通过彩色琼斯多项式计算扭结的复杂体积

• 发表时间: 2010
• 期刊: J. Knot Theory Ramifications
• 作者: Cho;Jinseok ; Murakami;Jun
• 通讯作者: Jun

Quantum 6j-symbols for nonintegral highest weight representations of U_q(sl_2) at root of unity

单位根处 U_q(sl_2) 的非整数最高权重表示的量子 6j 符号

• 发表时间: 2012
• 作者: Kurokiba;Masaki; Tanaka;Naoto; Tani;Atusi;金子和雄;大塚浩史;Hiroki Ohwa;金子 和雄;Taichiro Takagi;村上順
• 通讯作者: 村上順

On the relation between projective representations of Uq(s12) and hyperbolic volume

论Uq(s12)的射影表示与双曲体积的关系

• 发表时间: 2010
• 作者: 高橋弘充;河野貴文;釜江常好 他;Hiroki Ohwa;村上順
• 通讯作者: 村上順

Optimistic limits of the colored Jones polynomials

有色琼斯多项式的乐观极限

• DOI: 10.4134/jkms.2013.50.3.641
• 发表时间: 2013
• 期刊: J. Korean Math. Soc.
• 作者: Jinseok Cho;Jun Murakami
• 通讯作者: Jun Murakami