We prove a Chevalley formula for anti-dominant weights in the torus-equivariant K-group of semi-infinite flag manifolds, which is described explicitly in terms of semi-infinite Lakshmibai-Seshadri paths (or equivalently, quantum Lakshmibai-Seshadri paths); in contrast to the Chevalley formula for dominant weights in our previous paper [17], the formula for anti-dominant weights has a significant finiteness property. Based on geometric results established in [17], our proof is representation-theoretic, and the Chevalley formula for anti-dominant weights follows from a certain identity for the graded characters of Demazure submodules of a level-zero extremal weight module over a quantum affine algebra; in the proof of this identity, we make use of the (combinatorial) standard monomial theory for semi-infinite Lakshmibai-Seshadri paths, and also a string property of Demazure-like subsets of the set of semi-infinite Lakshmibai-Seshadri paths of a fixed shape, which gives an explicit realization of the crystal basis of a level-zero extremal weight module.

我们证明了圆环等效K 中反支配权重的 Chevalley 公式- 半无限标志流形组，根据半无限 Lakshmibai-Seshadri 路径（或等效的量子 Lakshmibai-Seshadri 路径）进行明确描述；与我们之前论文 [17] 中主导权重的 Chevalley 公式相比，反主导权重的公式具有显着的有限性。基于 [17] 中建立的几何结果，我们的证明是表示理论的，反支配权重的 Chevalley 公式遵循量子仿射上零级极值权重模块的 Demazure 子模块的分级特征的某个恒等式代数；在证明这种身份时，我们利用（组合）标准单项式理论，用于半无限 Lakshmibai-Seshadri 路径，