Littlewood-Richardson系数、Springer纤维与诱导表示的零化簇
Littlewood-Richardson Coefficient, Springer Fibers and the Annihilator Varieties of Induced Representations
AI总结：
本文利用几何Sakate等价证明了$GL(n,\mathbb{C})$中幂零轨道的包含关系与Littlewood-Richardson系数非零的等价性，并描述了用于研究Whittaker支撑和零化簇的空间$\mathcal{O}\cap\mathfrak{p}$的几何性质。
摘要：
对于$G=GL(n,\mathbb{C})$及具有双块Levi子群$L=GL(n_1)\times GL(n_2)$的抛物子群$P=LN$，空间$G\cdot (\mathcal{O}+\mathfrak{n})$（其中$\mathcal{O}$是$\mathfrak{l}$的幂零轨道）是$\mathfrak{g}$的幂零轨道的并集。在主定理的第一部分，我们利用几何Sakate等价证明$\mathcal{O'}\subset G\cdot (\mathcal{O}+\mathfrak{n})$当且仅当某些Littlewood-Richardson系数不为零。主定理的第二部分描述了空间$\mathcal{O}\cap\mathfrak{p}$的几何性质，该空间是研究$G$的表示的Whittaker支撑和零化簇的重要空间。
英文摘要：
For $G=GL(n,\mathbb{C})$ and a parabolic subgroup $P=LN$ with a two-block Levi subgroup $L=GL(n_1)\times GL(n_2)$, the space $G\cdot (\mathcal{\mathcal{O}}+\mathfrak{n})$, where $\mathcal{O}$ is a nilpotent orbit of $\mathfrak{l}$, is a union of nilpotent orbits of $\mathfrak{g}$. In the first part of our main theorem, we use the geometric Sakate equivalence to prove that $\mathcal{O'}\subset G\cdot (\mathcal{\mathcal{O}}+\mathfrak{n})$ if and only if some Littlewood-Richardson coefficients do not vanish. The second part of our main theorem describes the geometry of the space $\mathcal{O}\cap\mathfrak{p}$, which is an important space to study for the Whittaker supports and annihilator varieties of representations of $G$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
