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Weyl module

Weyl 模

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Introduction to Mathematical Logic, Sixth Edition 封面

《Introduction to Mathematical Logic, Sixth Edition》 · 第 413 页 · Chapter 9,Section 9.3.2「Weyl Modules」,Theorem 9.3.10

Theorem 9.3.10. Let $\lambda$ be a partition of $k$ with at most $n$ parts. If $A$ is a tableau of shape $\lambda$, then the operator $p_A = (\dim G_\lambda / k!) s(A)$ projects $\bigotimes^k \mathbb C^n$ onto an irreducible $\mathrm{GL}(n,\mathbb C)$-module with highest weight $\lambda$. [...] The subspace $p_A(\bigotimes^k \mathbb C^n)$ of $\bigotimes^k \mathbb C^n$ is called the Weyl module defined by the tableau $A$.

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