发表机构
Instituto Politécnico Nacional; University of Ostrava; Charles University; VSB–Technical University of Ostrava（国立理工学院; 俄斯特拉发大学; 查理大学; 俄斯特拉发科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究例外超维数下的正交辛不变超球面积分，通过生成函数及洛朗展开得到相关系数，恢复超空间对偶结构，建立广义调和模配对，推导协变符号并确定投影障碍。
AI 中文摘要
我们研究在例外超维数\(M = -2u\)下的正交辛不变超球面积分，此时调和菲舍尔结构变为非半单的且皮泽蒂配对退化。对于亚纯延拓的齐次逆核，我们得到生成函数\(\mathscr G_\mu(\rho;x,y) =\frac{\Gamma(\mu/2)}{2\pi^{\mu/2}} \bigl(1+\rho\{x,y\}+\rho^2x^2y^2\bigr)^{-\mu/2}\)。在\(\mu = -2u\)时，其洛朗展开有多项式留数和对数有限部分。我们证明这些系数恢复了具有非零玻色维数的固定超空间上的完整逐次对偶结构。在次数\(k\leq u\)时，留数反转\(\mathcal P_k\)上的规范重整化配对；在碰撞范围\(u < k\leq2u\)时，普通配对的根为\((x^2)^{k - u}\mathcal P_{2u - k}\)，有限部分再现商，留数从反射次数传输后再现根；对于\(k\geq2u + 1\)，有限部分是普通逆核。我们还建立了广义调和模上的非退化头 - 基座配对。作为应用，我们推导协变右 - 左径向\(q\) - 单源带状符号，并确定通过单侧\(q\) - 菲舍尔投影转移标量皮泽蒂再现的精确一次障碍。
英文摘要
We study orthosymplectically invariant supersphere integration at the exceptional superdimensions $M=-2u$, where the harmonic Fischer structure becomes nonsemisimple and the Pizzetti pairing degenerates. For the meromorphically continued homogeneous inverse kernels we obtain the generating function $$ \mathscr G_μ(ρ;x,y) =\frac{Γ(μ/2)}{2π^{μ/2}} \bigl(1+ρ\{x,y\}+ρ^2x^2y^2\bigr)^{-μ/2}. $$ At $μ=-2u$, its Laurent expansion has a polynomial residue and a logarithmic finite part. We prove that these coefficients recover the complete degreewise duality structure on a fixed superspace with nonzero bosonic dimension. In degrees $k\le u$, the residue inverts a canonical renormalized pairing on $\mathcal P_k$. In the collision range $u<k\le2u$, the ordinary pairing has radical $(x^2)^{k-u}\mathcal P_{2u-k}$; the finite part reproduces the quotient, while the residue reproduces the radical after transport from the reflected degree. For $k\ge2u+1$, the finite part is the ordinary inverse kernel. We also establish the nondegenerate head--socle pairing on the generalized harmonic modules. As an application, we derive covariant right--left radial $q$-monogenic zonal symbols and identify precise degree-one obstructions to transferring scalar Pizzetti reproduction through a one-sided $q$-Fischer projection.
