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I want to create a key binding like C-c C-f C-c to get \mathscr{} inside math environment. This is because there is no default key binding for getting \mathscr. How to do this? Remember that C-c C-f C-c is already in use to get \textsc in the text mode.

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Customize LaTeX-font-list: M-x customize-variable RET LaTeX-font-list RET. Select Math Prefix: for ^C key (the prefix C-c C-f is omitted) and add \mathscr{ to "Math Prefix:" field and } to "Math Suffix".

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