Modular representation theory is a branch of mathematics and that part of representation theory that studies linear representations of finite groups over a field k of positive characteristic as well as having applications to group theory modular representations arise naturally in other branches of mathematics such as algebraic geometry . The representation theory of finite groups can be approached from several points of view one can use the classical group theory or character theory approach keeping the group properties readily at hand or use ring theory or use module theory with emphasis either on the associated rings or algebras or the corresponding category of modules. This month long program is devoted to the representation theory over a field of nonzero characteristic of finite and p adic groups as well as related algebras especially those arising naturally in lie theory. Modular representation theory of finite groups a modular representation of a group is a homomorphism from the group to a matrix group over a field with positive characteristic p representation theory is the study of the various representations of a group
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