Deligne categories as limits in rank and characteristic
Deligne categories as limits in rank and characteristic
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德利涅类别作为等级和特征的限制
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发表时间：
2016
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通讯作者：
Nate Harman
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作者：
Nate Harman
利用大特征大秩一般线性群和对称群的模表示，给出了$mathbb{C}$上Deligne范畴$underline{Rep}（GL_t）$和$underline{Rep}（S_t）$（及其交换包络）的新的解释.特别地，我们理解了句子“$underline{Rep}（S_n）$ is the limit of $Rep（S_{p+n}）$ over $”当$p$趋于无穷大时，ar{mathbb{F}}_p$“。然后，我们给出了如何在这些不同设置之间传递结果的示例。
We give new interpretations of the Deligne categories $underline{Rep}(GL_t)$ and $underline{Rep}(S_t)$ (and their abelian envelopes) over $mathbb{C}$ in terms of modular representations of general linear and symmetric groups of large rank in large characteristic. In particular we make sense of the sentence "$underline{Rep}(S_n)$ is the limit of $Rep(S_{p+n})$ over $ar{mathbb{F}}_p$ as $p$ goes to infinity". We then give examples of how to pass results between these different settings.