When Om is written out as three sounds rather than as a single ligature, u stands in the middle, between a and m. The Mandukya Upanishad is the text that develops that analysis furthest, taking the syllable apart and correlating each of its three parts with a state of consciousness: a with waking, u with dream, m with deep sleep, and the silence that follows with a fourth state it does not name except as the fourth.
Later commentary built extensively on that scheme, and it is the source of most of the further correspondences attached to the syllable in the Vedantic literature. The correlation belongs to that text and its tradition of commentary, and this atlas records it as theirs. Sanskrit grammar contributes a second reason the sound sits where it does in the syllable. Under the rules by which vowels combine, a followed by u yields the diphthong o, so the written form of Om is the outcome of the same rule that operates everywhere else in the language, and its three-part analysis is a reading back of the syllable into the sounds that would have produced it.
In the Tantric arrangement of the letters, u belongs with the other vowels to the class held to precede the consonants, and it is one of the fifty matrika counted in the garland. Individual schools attach further attributions to it; those attributions are the schools', and are described in the scholarly literature rather than harmonised by it.