Tag Archives: schur’s lemma

Polynomials and Representations XXVIII

Starting from this article, we will look at representations of . Now, itself is extremely complicated so we will only focus on representations of particular types. Generally, for any topological group G, we want: to be a continuous homomorphism of groups. Continuous … Continue reading

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Simple Modules

We briefly talked about modules over a (possibly non-commutative) ring R. An important aspect of modules is that unlike vector spaces, modules are usually not free, i.e. they don’t have a basis. For example, take the Z-module given by Z/2Z. [ Recall: a Z-module is … Continue reading

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Quick Guide to Character Theory (II): Main Theory

Reminder: throughout this series, G is a finite group and K is a field. All K-vector spaces are assumed to be finite-dimensional over K. G4. Maschke’s Theorem If is a K[G]-submodule, it turns out V is isomorphic to the direct sum of W and some other submodule W’. … Continue reading

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