论文标题
Littlewood-Richardson系数，Springer纤维和诱发表示形式的歼灭器品种
Littlewood-Richardson Coefficient, Springer Fibers and the Annihilator Varieties of Induced Representations
论文作者
论文摘要
对于$ g = gl（n，\ mathbb {c}）$和一个抛物线子组$ p = ln $，带有两个块Levi子组$ l = gl（n_1）\ times gl（n_2）$，space $ g \ cdot（\ cdot（\ cdot） $ \ mathcal {o} $是$ \ mathfrak {l} $的nilpotent轨道，是$ \ mathfrak {g} $的nilpotent轨道的结合。在我们的主要定理的第一部分中，我们使用几何sakate等价来证明$ \ MATHCAL {O'} \ subset g \ cdot（\ Mathcal {\ Mathcal {\ Mathcal {o}}}+\ Mathfrak {n}）$ if，并且仅在某些Littlewood-Richardon Coeff do van and vansish。我们主要定理的第二部分描述了空间的几何形状$ \ mathcal {o} \ cap \ mathfrak {p} $，这是$ g $的惠特克支持和歼灭者的重要空间。
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 $G$.
