论文标题
倒数$ K $ -CHEVALLEY公式用于半无限旗歧管，I：ADE类型的微小权重
Inverse $K$-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type
论文作者
论文摘要
我们证明了Equivariant $ k $ - 简单类型的半无限标志歧管理论中的显式逆转雪佛兰公式。通过逆雪瓦利公式，我们的意思是用schubert类的量产物的乘积公式，以$ \ mathbb {z} [q^{\ pm 1}] $ - schubert类别的线性组合扭曲了Equivariant Line Line Bundles。我们的公式适用于简单类型和epariant标量$ e^λ$的半无限标志歧管中的任意Schubert类，其中$λ$是任意的缩小重量。由于Stembridge的结果，我们的公式完全确定了以简单类型的任意权重的逆雪瓦利公式，除了类型$ e_8 $。我们公式的组合学是由量子bruhat图控制的，并且证明是基于双仿射Hecke代数的限制。因此，我们的公式还提供了所有非对称$ Q $ -TODA操作员的明确确定，用于ADE类型的微小权重。
We prove an explicit inverse Chevalley formula in the equivariant $K$-theory of semi-infinite flag manifolds of simply-laced type. By an inverse Chevalley formula, we mean a formula for the product of an equivariant scalar with a Schubert class, expressed as a $\mathbb{Z}[q^{\pm 1}]$-linear combination of Schubert classes twisted by equivariant line bundles. Our formula applies to arbitrary Schubert classes in semi-infinite flag manifolds of simply-laced type and equivariant scalars $e^λ$, where $λ$ is an arbitrary minuscule weight. By a result of Stembridge, our formula completely determines the inverse Chevalley formula for arbitrary weights in simply-laced type, except for type $E_8$. The combinatorics of our formula is governed by the quantum Bruhat graph, and the proof is based on a limit from the double affine Hecke algebra. As such, our formula also provides an explicit determination of all nonsymmetric $q$-Toda operators for minuscule weights in ADE type.
