论文标题
$ \ Mathcal {u} _Q的抛物线阳性表示（\ Mathfrak {g} _ \ Mathbb {r}）$
Parabolic Positive Representations of $\mathcal{U}_q(\mathfrak{g}_\mathbb{R})$
论文作者
论文摘要
我们构建了$ \ mathcal {u} _q（\ Mathfrak {g} _ \ Mathbb {r}）$及其模块化双重及其模块化双重的新家族，通过量化与任意抛物线子组的经典抛物线诱导，以使其与任意抛物线子组相对应，以使其生成的经典抛物线诱导，从而使其模块化双群，从$ \ mathcal {u} _q（\ mathfrak {g} _ \ mathbb {r}）$由正面的自偶会操作员在希尔伯特（Hilbert）空间上行动。这概括了公认的积极表示，这与最小抛物线（即Borel）亚组的诱导相对应。我们还详细研究了$ a_n $类型的特殊情况，其作用于$ l^2（\ mathbb {r}^n）$具有最小的功能维度，并建立其中心字符的属性和通用$ \ Mathcal {r} $ operator。我们构建了仿射量子组$ \ MATHCAL {u} _Q（\ wideHat {\ Mathfrak {\ Mathfrak {sl}} _ {n+1}）$的阳性版本。
We construct a new family of irreducible representations of $\mathcal{U}_q(\mathfrak{g}_\mathbb{R})$ and its modular double by quantizing the classical parabolic induction corresponding to arbitrary parabolic subgroups, such that the generators of $\mathcal{U}_q(\mathfrak{g}_\mathbb{R})$ act by positive self-adjoint operators on a Hilbert space. This generalizes the well-established positive representations which corresponds to induction by the minimal parabolic (i.e. Borel) subgroup. We also study in detail the special case of type $A_n$ acting on $L^2(\mathbb{R}^n)$ with minimal functional dimension, and establish the properties of its central characters and universal $\mathcal{R}$ operator. We construct a positive version of the evaluation module of the affine quantum group $\mathcal{U}_q(\widehat{\mathfrak{sl}}_{n+1})$ modeled over this minimal positive representation of type $A_n$.
