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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6320 • Algebra II

Summer 2021 • Question 5

Question

Math 6320 • Algebra II Summer 2021 • Question 5

Suppose \(\sigma \) and \(\tau \) are two elements of \(A_5\) such that, for every finite dimensional complex representation \(\rho \) of \(S_5\), \(\chi _\rho (\sigma )=\chi _\rho (\tau )\) (here \(\chi _\rho \) denotes the character of \(\rho \)). Are \(\sigma \) and \(\tau \) conjugate in \(A_5\)?

Raw LaTeX

Suppose \(\sigma\) and \(\tau\) are two elements of \(A_5\) such that, for every
finite dimensional complex representation \(\rho\) of \(S_5\),
\(\chi_\rho(\sigma)=\chi_\rho(\tau)\) (here \(\chi_\rho\) denotes the character
of \(\rho\)). Are \(\sigma\) and \(\tau\) conjugate in \(A_5\)?

Topic Tags

Character Theory Finite Group Theory Representation Theory Symmetric and Alternating Groups