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Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
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Char $p$ representations of $SL_2(\mathbb{F}_p)$ and $GL_2(\mathbb{F}_p)$
It is a well known fact that the irreducible representations of $SL_2(\mathbb{F}_p)$ over $\overline{\mathbb{F_p}}$ are given by the symmetric powers $Symm^k(V)$, where $V = \overline{\mathbb{F}_p}^2$ …