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Apr 21'25
[math] \newcommand{\mathds}{\mathbb}[/math]

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Prove that the bistochastic groups [math]B_N\subset O_N[/math] and [math]C_N\subset U_N[/math], consisting of matrices having sum [math]1[/math] on each row and column, are both easy.

Apr 21'25
[math] \newcommand{\mathds}{\mathbb}[/math]

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Look up the full theory of the symplectic group [math]Sp_N\subset U_N[/math], namely Brauer theorem, super-easiness, and Weingarten formula.