# Questions tagged [frobenius-schur-indicator]

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### Frobenius-Schur indicator of a self-dual L-parameter

Let $F$ be a non-archimedean field and let $\pi$ be a self-dual supercuspidal representation of $\mathrm{GL}_n(F)$ (which, by a result of Adler exists only when $n=1$ or $n$ is even). Then, under LLC ...
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### Counting adjoints in the symmetric or antisymmetric square of a Lie group representation

EDIT (November 1, 2022): Over the weekend I think I found a technique to determine the exact multiplicities, according to how conjugation acts on the fundamental weights. While I haven't done the ...
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### Second Frobenius-Schur indicator and near-group categories G+|G|

A near-group category $G+m$ is a (spherical) fusion category whose simple objects are given by the element $g$ of the finite group $G$, plus one extra simple object $y$, with Grothendieck ring as ...
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### A property forcing the Frobenius-Schur indicator to be positive

Let $G$ be a finite group. Two irreducible complex representations $V,V'$ of $G$ are called dual to each other if $V \otimes V'$ admits a trivial component, i.e. $\hom_G(V \otimes V',V_0)$ is positive ...
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### Is $1\neq a\in Z(2.E_7(q))\cong Z_2$ a square element in $2.E_7(q)$?

When $q$ is a power of some odd prime, is $1\neq a\in Z(2.E_7(q))\cong Z_2$ a square element in $2.E_7(q)$? A Lie algebra is a vector space $L$ over a field $K$ on which a product operation $[xy]$ is ...
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### 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 ...
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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 \$...