论文标题
部分可观测时空混沌系统的无模型预测
Ghost center and representations of the diagonal reduction algebra of $\mathfrak{osp}(1|2)$
论文作者
论文摘要
减少代数以文献中的许多名称为名，包括步骤代数，Mickelsson代数，Zhelobenko代数和TransVector代数，仅举几例。这些代数是通过升高和降低操作员实现的，允许计算Clebsch-Gordan系数，分支规则和交织运算符；并与可集成面部模型中的极端方程式和动力学R型联系在一起。 在本文中，我们继续研究对角线减少级别的of of themplectic lie superalgebra $ \ mathfrak {osp}（1 | 2）$。我们构建了Harish-Chandra同态，Verma模块，并在每个Verma模块上研究Shapovalov形式。使用这些结果，我们证明了$ a $的幽灵中心（中心加反中心）是由两个中央元素和一个反中央元素（类似于scasimir fyLeśniewski，forLeśniewskifor $ \ mathfrak {osp {osp}（1 | 2）$）产生的。作为另一个应用程序，我们将$ a $的所有有限维不可约定表示形式分类。最后，我们明确计算无限量张量产品分解。
Reduction algebras are known by many names in the literature, including step algebras, Mickelsson algebras, Zhelobenko algebras, and transvector algebras, to name a few. These algebras, realized by raising and lowering operators, allow for the calculation of Clebsch-Gordan coefficients, branching rules, and intertwining operators; and have connections to extremal equations and dynamical R-matrices in integrable face models. In this paper we continue the study of the diagonal reduction superalgebra $A$ of the orthosymplectic Lie superalgebra $\mathfrak{osp}(1|2)$. We construct a Harish-Chandra homomorphism, Verma modules, and study the Shapovalov form on each Verma module. Using these results, we prove that the ghost center (center plus anti-center) of $A$ is generated by two central elements and one anti-central element (analogous to the Scasimir due to Leśniewski for $\mathfrak{osp}(1|2)$). As another application, we classify all finite-dimensional irreducible representations of $A$. Lastly, we calculate an infinite-dimensional tensor product decomposition explicitly.
