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Let $k=(k_1,k_2,k_3,k_4)\in \mathbb{N}^4$ and let $s_k(x_1,x_2,x_3,x_4)$ be the Schur polynomial on $GL_4$. Question 1: If I replace $x_3$ with $x_1$ and $x_4$ with $x_2$, can $s_k(x_1,x_2,x_1,x_2)$ ...