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This tag is used if a reference is needed in a paper or textbook on a specific result.
7
votes
Decomposition of symmetric powers of the fundamental representation of $\text{Sp}(2n,\mathbb...
Yes, it is just $\operatorname{Sym}^k(V)$ itself.
Specifically: Let $V = \mathbb{C}^{2n}$ be the natural module for $Sp(2n, \mathbb{C})$. Then for all $k \geq 1$, the symmetric power $\operatorname{Sy …
5
votes
Existence of a regular semisimple element over $\mathbb{F}_{q}$
(Edit: the previous version of this answer was not correct, but I leave this here as a remark)
Let $\sigma: G \rightarrow G$ be the Frobenius map corresponding to the field automorphism $x \mapsto x^q …