Itô's theorem

Itô's theorem is a result in the mathematical discipline of representation theory due to Noboru Itô. It generalizes the well-known result that the dimension of an irreducible representation of a group must divide the order of that group.

This article is about the result in representation theory. For the result in stochastic calculus, see Itô's lemma.

Statement

Given an irreducible representation V of a group G and a maximal normal abelian subgroup A ⊆ G, the dimension of V must divide [A:G].

gollark: There are some which do, but they have different constraints.
gollark: Nope.
gollark: Ranked voting systems are subject to the horrors of Arrow's impossibility theorem.
gollark: Do vote gollark. Maybe vote palaiologos.
gollark: I said "and".

References
  • James, Gordon; Liebeck, Martin (1993). Representations and Characters of Groups. Cambridge University Press. p. 247. ISBN 0 521 44590 6.
  • Weisstein, Eric. "Itô's Theorem". Wolfram Mathworld. Wolfram Research. Retrieved 6 November 2018.


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