Enter Unicode characters with 8-digit hex code

You can use <C-v>U, that is, an uppercase u, to input an 8 digit hex codepoint character.

More information here and here.

There exists a Unicode plugin for Vim. According to the plugin description, this plugin has three main features:

1. Character/digraph completion using either the Unicode name or the codepoint.
2. Identify the character/digraph under the cursor.
3. Search for digraphs by name; transform two normal characters into their corresponding digraph.

There is a Vim feature designed to simplify entering characters that cannot be typed directly. It is called Digraphs (see :help digraphs).

To define a custom digraph for entering ‘𝓭’, use an Ex command similar to the one below.

:dig dd 120045

where 120045 is the decimal representation of ‘𝓭’, as one can easily confirm using the ga command.

Inserting a character using a digraph is simple: Type Ctrl+K followed by the shortcut of that digraph (dd for the above example).