论文标题
拓扑量子场理论的Hecke组的射影表示
Projective representations of Hecke groups from Topological quantum field theory
论文作者
论文摘要
我们构建了与较高属表面的witten-Reshetikhin-turaev拓扑量子场理论相关的Hecke群体的投影（统一）表示。特别是，我们概括了Temperley-Lieb-Jones模块化类别的模块化数据。我们还研究了表示形式的一些特性。我们显示，通过显式计算，表示表示形式的图像组在属$ 2 $中是无限的。我们还显示，当级别等于$ 4L+2 $的$ l \ geq 1 $时，该表示形式至少可以降低三个不可约的求和。
We construct projective (unitary) representations of Hecke groups from the vector spaces associated with the Witten-Reshetikhin-Turaev topological quantum field theory of higher genus surfaces. In particular, we generalize the modular data of Temperley-Lieb-Jones modular categories. We also study some properties of the representation. We show the image group of the representation is infinite at low levels in genus $2$ by explicit computations. We also show the representation is reducible with at least three irreducible summands when the level equals $4l+2$ for $l\geq 1$.
