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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6320 • Algebra II

Summer 2025 • Question 4

Question

Math 6320 • Algebra II Summer 2025 • Question 4

Let \(G\) be a finite group. Let \(V_1\) and \(V_2\) be two non-isomorphic irreducible complex representations. Let \(V = V_1 \oplus V_2\). Compute the algebra of linear transformations of \(V\) intertwining the action of \(G\): \[ \operatorname {Hom}_G(V,V). \]

Raw LaTeX

Let \(G\) be a finite group. Let \(V_1\) and \(V_2\) be two non-isomorphic
irreducible complex representations. Let \(V = V_1 \oplus V_2\). Compute the
algebra of linear transformations of \(V\) intertwining the action of \(G\):
\[
\operatorname{Hom}_G(V,V).
\]

Topic Tags

Finite Group Theory Irreducible Polynomials Representation Theory