<inline-formula><tex-math id="M2">\begin{document}${\frak s}{\frak l}(n+1)$\end{document}</tex-math></inline-formula>的次正则幂零表示的同态空间

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${\frak s}{\frak l}(n+1)$的次正则幂零表示的同态空间

基金项目: 国家自然科学基金（11671138）；新疆维吾尔自治区自然科学基金（2016D01A014）

1.
School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China
2.
School of Mathematical Sciences, East China Normal University, Shanghai 200241, China

摘要: 令李代数${\frak g}={\frak s}{\frak l}(n+1)$的基域是特征为素数$p$的代数闭域$\textbf{k}$且满足$p\nmid n+1$.本文在${\frak g}$的次正则幂零表示中, 证明了相同块中的任意两个小Verma模的同态是非零的.这揭示了小Verma模之间的完整联系.
- 标准Levi型 /
- 小Verma模 /
- 次正则幂零 /
- 同态空间
Abstract: Let ${\frak g}={\frak {sl}}(n+1)$ be the special linear Lie algebra over an algebraically closed field $\textbf{k}$ of prime characteristic $p$ with $p \nmid n+1$. We show that the hom-spaces between any two baby Verma modules in the same given block are always nonzero for subregular nilpotent representations of $\frakg$, which reveals a complete linkage atlas for baby Verma modules.
- standard Levi-form /
- baby Verma module /
- subregular nilpotent /
- homspaces

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[4]	JANTZEN J C. Representations of Lie algebras in prime characteristic[C]//Proceedings of Representation Theories and Algebraic Geometry. Montreal: NATO ASI, 1997.

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