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"text": "Woit 在第16.1节把实辛群描述为作用在 $\\mathcal M=\\mathbf R^{2d}$ 上、保持决定相空间辛几何的反对称双线性形式 $\\Omega$ 的线性变换群，其保形式条件写为：\n\n\n\n$$\n\\Omega (g v _ {1}, g v _ {2}) = \\Omega (v _ {1}, v _ {2})\n$$\n\n",
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"summary": "第16.1节以保持决定相空间辛几何的反对称双线性形式的线性变换来界定 $Sp(2d,\\mathbf R)$。随后作者把作用从 $\\mathcal M$ 传到由 $\\Omega(u,\\cdot)$ 表示的线性函数，并将式 (16.1) 写为：\n\n\n\n$$\n\\Omega (u, \\cdot) \\in M \\to g \\cdot \\Omega (u, \\cdot) = \\Omega (u, g ^ {- 1} (\\cdot)) = \\Omega (g u, \\cdot) \\in M\\tag{16.1}\n$$\n\n\n\n作者说明第一个等号来自对偶表示的定义，第二个等号来自 $\\Omega$ 的不变性。",
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"conditions": "Szekeres 的矩阵为 $2n\\times2n$ 实矩阵，$\\mathsf J$ 的分块由零矩阵和单位矩阵组成。",
"notation": "保留原书写法 $Sp(2n)$、$\\mathsf A$、$\\mathsf J$；Woit 该节写作 $Sp(2d,\\mathbf R)$。",
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