发表机构
Center for Quantum Mathematics, University of Southern Denmark（南丹麦大学量子数学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过扩展Dirac方法并利用修正的Dirac不等式与超Freudenthal递归，确定了基本经典李超代数在偶数子代数限制下的酉分支，给出了分支重数的闭式公式及酉性刻画。
AI 中文摘要
我们确定了基本经典李超代数 $\mathfrak{sl}(m|n)$、$\mathfrak{osp}(m|2n)$ 和 $F(4)$ 的不可约酉表示在限制到其偶数子代数时的分支。证明结合了 Huang-Pandžić-Dirac 算子 $\operatorname{D}_{\mathfrak{g},\mathfrak{g}_{\bar{0}}}$ 的 Dirac 不等式与从 Dirac 形式导出的 Freudenthal 递归的超模拟。我们通过奇数反射传递 Dirac 不等式并确定由此产生的修正项，将 Dirac 方法扩展到不适配于相关实形式的正根系。这产生了有限的递归过程，确定出现的偶数成分及其分支重数，并给出后者的闭式公式，且统一适用于任意非典型度。对于 $\mathfrak{sl}(m|n)$，修正后的 Dirac 不等式还给出了所有与酉表示相关的正根系的酉性刻画。
英文摘要
We determine the branching of irreducible unitary representations of the basic classical Lie superalgebras $\mathfrak{sl}(m|n)$, $\mathfrak{osp}(m|2n)$, and $F(4)$ under restriction to their even subalgebras. The proof combines Dirac inequalities for the Huang-Pandžić-Dirac operator $\operatorname{D}_{\mathfrak{g},\mathfrak{g}_{\bar{0}}}$ with a super analogue of Freudenthal's recursion derived from the Dirac formalism. We extend the Dirac method to positive systems that are not adapted to the relevant real form by transporting the Dirac inequality through odd reflections and determining the resulting correction terms. This yields finite recursive procedures that determine the occurring even constituents and their branching multiplicities, together with closed formulas for the latter, uniformly in the degree of atypicality. For $\mathfrak{sl}(m|n)$, the corrected Dirac inequalities also give a characterization of unitarity for all positive systems relevant to unitary representations.
Comments54 pages; comments are welcome
