受限正交群 / Restricted orthogonal group

Woit · §39.2 The restricted symplectic group

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英文 OCR 草稿

Preserves the author-printed commutator [J_g,J_0] criterion. Mathematical adequacy of this condition is separately pending; this machine reading source is not default original evidence.

机器草稿中的定义提及

Definition (Restricted symplectic and orthogonal groups)

The group of linear transformations g of an infinite dimensional symplectic vector space preserving the symplectic structure and also satisfying the condition

$$tr(A^{†}A)<\infty$$

on the operator

$$A=[J_g,J_0]$$

is called the restricted symplectic group and denoted $S{p}_{res}$ . The group of linear transformations g of an infinite dimensional inner-product space preserving the inner-product and satisfying the same condition as above on $[J_g,J_0]$ is called the restricted orthogonal group and denoted $S{O}_{res}$

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来源与版本

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正文：英文 OCR 草稿

来源版本：2025-10-20

原文位置：§39.2；PDF 页 437；印刷页 420

处理记录：MinerU OCR

核对状态：英文 OCR 草稿 · 待校对

中文机译草稿

Preserves the author-printed commutator [J_g,J_0] criterion. Mathematical adequacy of this condition is separately pending; this machine reading source is not default original evidence.

机器草稿中的定义提及

定义（限制辛群与正交群）

无限维辛向量空间上保持辛结构并同时满足该条件的线性变换 $g$ 构成的群

$$tr(A^{†}A)<\infty$$

关于该算符

$$A=[J_g,J_0]$$

称为限制辛群，记作 $S{p}_{res}$。无限维内积空间上保持内积并满足与上述关于 $[J_g,J_0]$ 相同条件的线性变换 $g$ 构成的群称为限制正交群，记作 $S{O}_{res}$。

阅读所在节 · 完整章节

来源与版本

查看 PDF

正文：中文机译草稿

来源版本：2025-10-20

原文位置：§39.2；PDF 页 437；印刷页 420

处理记录：MinerU OCR；machine-translation/deepseek-v4.1-flash

核对状态：中文机译草稿 · 待校对