论文标题
Ado不变性是一个Q-Onolonic家族
The ADO Invariants are a q-Holonomic Family
论文作者
论文摘要
我们研究了基于量子组的量子群的量子群的$ q $ - 单位属性，其量子尺寸消失了，这是由于搜索不变式物理学的实现而激发的。这种类型的一些最著名的不变式，由$ 2R $ - $ 2R $的Unity（\ Mathfrak {slfrak {sl} _2）$以$ 2R $的Unity的unity（\ Mathfrak {slfrak {sl} _2）$构建的“典型”表示$ \ Mathcal u^h_ {ζ_{ζ_{ζ_{2r}}（\ Mathfrak {sl} _2 _2）$ - 由Akutsu-deguchuchi-deguchi-deguchi-i-ohohtss od to我们证明，$ r \ geq 2 $的ado不变性是一个$ q $ - 单位家族，尤其意味着它们满足独立于$ r $的递归关系。就结一个而言，我们证明了Ado不变的$ Q $ - 单位递归理想，其中包含在有色琼斯多项式的递归理想中，这是著名的AJ猜想的主题。 （结合最新的Willett的结果，这建立了Ado和Jones递归理想的同构。我们的结果还证实了Gukov-Hsin-Nakajima-Pakar-Pei-Pei-pei-Sopenko的最新物理动机猜想。）
We investigate the $q$-holonomic properties of a class of link invariants based on quantum group representations with vanishing quantum dimensions, motivated by the search for the invariants' realization in physics. Some of the best known invariants of this type, constructed from `typical' representations of the unrolled quantum group $\mathcal U^H_{ζ_{2r}}(\mathfrak{sl}_2)$ at a $2r$-th root of unity, were introduced by Akutsu-Deguchi-Ohtsuki (ADO). We prove that the ADO invariants for $r\geq 2$ are a $q$-holonomic family, implying in particular that they satisfy recursion relations that are independent of $r$. In the case of a knot, we prove that the $q$-holonomic recursion ideal of the ADO invariants is contained in the recursion ideal of the colored Jones polynomials, the subject of the celebrated AJ Conjecture. (Combined with a recent result of S. Willetts, this establishes an isomorphism of the ADO and Jones recursion ideals. Our results also confirm a recent physically-motivated conjecture of Gukov-Hsin-Nakajima-Park-Pei-Sopenko.)
