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In mathematics, more specifically in group theory, the character of a group representation is a function on the group which associates to each group element the trace of the corresponding matrix. The situation with representations over a field of positive characteristic, so-called "modular representations". Many deep theorems on the structure of finite groups use characters of modular representations.
Modular representation theory (character) is a branch of mathematics, and that part of representation theory that studies linear representations of finite group G over a field K of positive characteristic. Within finite group theory, character-theoretic results proved by Richard Brauer using modular representation theory played an important role in early progress towards the classification of finite simple groups.
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