论文标题
Schur-二元性二元性对交换戒指
Schur--Weyl duality over commutative rings
论文作者
论文摘要
Schur的经典案例 - weyl双重性指出，$ d^{th} $上的$ gl_n $和$ s_d $的组代数的动作 - 有限的自由模块相互集中的张量。我们表明，舒尔 - weyl二元性适用于换向环，可以选择足够的标量，其非零差异是可逆的。这意味着到目前为止，所有已知的Schur二元性案例。我们还表明，$ \ mathbb {z} $的schur-weyl二元性在$ d $足够大时都会失败。
The classical case of Schur--Weyl duality states that the actions of the group algebras of $GL_n$ and $S_d$ on the $d^{th}$-tensor power of a free module of finite rank centralize each other. We show that Schur--Weyl duality holds for commutative rings where enough scalars can be chosen whose non-zero differences are invertible. This implies all the known cases of Schur--Weyl duality so far. We also show that Schur--Weyl duality fails for $\mathbb{Z}$ and for any finite field when $d$ is sufficiently large.
