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  "body": "\n## Summary\n\nA bounded symmetric domain is a bounded domain $D$ in $\\C^n$ with many symmetries.\nAt each point $p$ of $D$ there is a holomorphic involution of $D$ with $p$ as an isolated fixed point.\nExamples are the unit ball, the polydisc and the bounded model of the [[Siegel upper half-space|5PTYE97PF6]].\nWith its Bergman metric, a bounded symmetric domain is a [[Hermitian symmetric space|NT4797Z9H8]] of noncompact type, and every such space arises in this way.\nCartan classified them, and they are the domains on which automorphic forms in several variables live.\n\n## Explanations\n\n### L1 human\n\nThe unit disc has a holomorphic \"point reflection\" $z \\mapsto -z$ through its centre, and by moving points around with Möbius maps it has one through every point.\nA bounded symmetric domain is a bounded region in several complex variables with the same property.\nThese reflections are so many that they move any point to any other, so the domain looks the same everywhere.\nProducts of discs and the unit ball in $\\C^n$ are basic examples.\n",
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