论文标题
半无限标志歧管和量子K理论的一般雪佛兰公式
A general Chevalley formula for semi-infinite flag manifolds and quantum K-theory
论文作者
论文摘要
我们给出了雪佛兰公式，用于用于圆环 - e e级$ k $ - 半灭旗歧管的特定权重，该公式是根据量子壁coder模型表示的。作为应用程序，我们证明了（小）torus-equivariant Quantum $ k $ -k $ -theory $ qk_ {t}（t}（g/b）$ a（普通的）flagorold $ g/b $（g/b）$的雪佛兰公式（小）torus-equivariant $ k $ - qk_ {t}（g/b）;这是关于$ qk_ {t}（g/b）$的乘法结构的长期猜想。在类型$ a_ {n-1} $中，我们证明所谓的量子grothendieck多项式确实代表（相反的）schubert类中的（非等级）量子$ k $ - theory $ k $ - qk（sl_ {n}/b）$;我们还获得了有关各个雪佛兰公式中系数的非常明确的信息。
We give a Chevalley formula for an arbitrary weight for the torus-equivariant $K$-group of semi-infinite flag manifolds, which is expressed in terms of the quantum alcove model. As an application, we prove the Chevalley formula for an anti-dominant fundamental weight for the (small) torus-equivariant quantum $K$-theory $QK_{T}(G/B)$ of an (ordinary) flag manifold $G/B$; this has been a longstanding conjecture about the multiplicative structure of $QK_{T}(G/B)$. In type $A_{n-1}$, we prove that the so-called quantum Grothendieck polynomials indeed represent (opposite) Schubert classes in the (non-equivariant) quantum $K$-theory $QK(SL_{n}/B)$; we also obtain very explicit information about the coefficients in the respective Chevalley formula.
