The elliptic Weyl character formula
The elliptic Weyl character formula
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椭圆Weyl特征公式
DOI：
10.1112/s0010437x1300777x
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发表时间：
2012
影响因子：
1.8
通讯作者：
Nora Ganter
中科院分区：
文献类型：
--
作者：
Nora Ganter
**摘要**：我们计算了部分旗簇$G/H$的等变椭圆上同调，其中$H\subseteq G$是等秩的紧连通李群。我们将$RO(G)$-分次系数${\mathcal{E}}ll_G^*$确定为卢伊延加（Looijenga）线丛的幂次，并证明沿着映射
$$\begin{equation*}
\pi \,{:}\,G/H\longrightarrow {\rm pt}
\end{equation*}$$
的转移是由外尔 - 卡茨（Weyl - Kac）特征公式计算的。通过并行处理普通上同调、$K$-理论和椭圆上同调，本文为[N. 甘特（N. Ganter）和A. 拉姆（A. Ram）所著《椭圆舒伯特演算（Elliptic Schubert calculus，准备中）》]的椭圆舒伯特演算组织了理论框架。
Abstract We calculate equivariant elliptic cohomology of the partial flag variety $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G/H$, where $H\subseteq G$ are compact connected Lie groups of equal rank. We identify the ${\rm RO}(G)$-graded coefficients ${\mathcal{E}} ll_G^*$ as powers of Looijenga’s line bundle and prove that transfer along the map $$\begin{equation*} \pi \,{:}\,G/H\longrightarrow {\rm pt} \end{equation*}$$ is calculated by the Weyl–Kac character formula. Treating ordinary cohomology, $K$-theory and elliptic cohomology in parallel, this paper organizes the theoretical framework for the elliptic Schubert calculus of [N. Ganter and A. Ram, Elliptic Schubert calculus, in preparation].