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16
votes
5answers
558 views

Is there a formula for the Frobenius-Schur indicator of a rep of a Lie group?

Let $G$ be a simple algebraic group group over $\mathbb C$. Let $V$ be a self-dual representation of $G$. Let $\lambda$ be the highest weight of $V$. Write $\lambda$ as a sum of fundamental weights: $...
2
votes
2answers
347 views

If all real conjugacy classes are strongly real, then all real irreps are “strongly real”(symmetric), true ?

Question Is true that if all real conjugacy classes of a finite group are strongly real, then all its real irreducible representations (irreps) are "strongly real"(symmetric) ? And vice verse ? ...
1
vote
1answer
250 views

sum_g g^k, Frobenius-Schur indicators, S_n-invariants in freeAss(x_i), center of the group algebra

For any $k$ sums $T_k = 1/|G|\sum_{g\in G} g^k$ belong to the center of the group algebra, for finite group G. For $k=2$ they "are" (up to details and interpretation) Frobenius-Schur indicators. For $...