We define the odd affine Temperley-Lieb algebra (OATLA) to be the category defined by planar diagrams in an annulus with an odd number of marked points on each boundary connected in pairs by disjoint strings and a modulus delta. This algebra is the odd part of the annularization of the Temperley-Lieb planar algebra. A positivity result is proved, which allows us to completely characterize the Hilbert space representations of OATLA when the parameter 6 is of the form 2 cos pi/N. The results finish the project of describing the irreducible Hilbert representations of the affine Temperley-Lieb algebra, which naturally arises in the study of subfactors.
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机译：我们将奇仿射Temperley-Lieb代数（OATLA）定义为圆环中的平面图定义的类别，每个边界上的奇数个标记点由不相交的字符串和模量增量成对连接。该代数是Temperley-Lieb平面代数环化的奇数部分。证明了一个阳性结果，当参数6的形式为2 cos pi / N时，这使我们能够完全表征OATLA的希尔伯特空间表示。结果完成了描述仿射Temperley-Lieb代数的不可约希尔伯特表示的项目，这在子因子的研究中自然而然地出现。
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