Limits of the quantum SO(3) representations for the one-holed torus
Limits of the quantum SO(3) representations for the one-holed torus
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单孔环面的量子 SO(3) 表示的极限
DOI：
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发表时间：
2012
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通讯作者：
Ramanujan Santharoubane
中科院分区：
文献类型：
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作者：
Ramanujan Santharoubane
对于$N geq 2$，我们研究了某个序列$（
ho_p^{（c_p）}）$，并证明了Andersen，Masbaum和Ueno的猜想对这些表示成立.这是通过证明，在一定的基础上，直到重新缩放，这些表示的矩阵收敛为p趋于无穷大。此外，极限描述了$SL_{2}（mathbb{Z}）$在二元齐次多项式空间上的作用，其总次数为$N-1$。
For $N geq 2$, we study a certain sequence $(
ho_p^{(c_p)})$ of N-dimensional representations of the mapping class group of the one-holed torus arising from SO(3)-TQFT, and show that the conjecture of Andersen, Masbaum, and Ueno cite{1} holds for these representations. This is done by proving that, in a certain basis and up to a rescaling, the matrices of these representations converge as $p$ tends to infinity. Moreover, the limits describe the action of $SL_{2}(mathbb{Z})$ on the space of homogeneous polynomials of two variables of total degree $N-1$.