论文标题
CHEVALLEY类型的身份，用于C型C型量子的零元素谱的分级字符的标识
Identities of inverse Chevalley type for graded characters of level-zero Demazure submodules over quantum affine algebras of type C
论文作者
论文摘要
我们为额定额定重量模块的零元素量元模块的分级字符提供了逆雪瓦利类型的身份，这是$ c $ type $ c $的量子仿射代数。这些身份表达产品$ e^μ\，\ mathrm {gch} \，v_ {x}^{ - }^{ - }（λ）（λ）$的（一维）字符$ e^μ$，其中$μ$是a（不一定是主导）natuscule的重量，具有毕业生$ \ gathrm mathrm {gch}， v_ {x}^{ - }（λ）$ a级零件的$ v_ $ v_ {x}}^{ - }^{ - }（λ）$上的量子仿射代数$ _ {\ mathsf {Q}}}零额定水平的分类的分级字符。这些身份立即暗示了半偶然的Flag歧管$ \ Mathbf {q} _ {Q} _ {g} $与与连接，简单相关的和简单的代数组$ g $ C $相关的半偶然旗帜歧管$ \ Mathbf {q} _ {g} $的相应逆雪瓦利公式。此外，如果$μ$是标准基础元素$ \ varepsilon_ {k} $，我们从$ g $ $ g $ $ g $ $ p $ $ p $中得出了从上方的chevalley类型的身份获得无取消身份。
We provide identities of inverse Chevalley type for the graded characters of level-zero Demazure submodules of extremal weight modules over a quantum affine algebra of type $C$. These identities express the product $e^μ \, \mathrm{gch} \, V_{x}^{-}(λ)$ of the (one-dimensional) character $e^μ$, where $μ$ is a (not necessarily dominant) minuscule weight, with the graded character $\mathrm{gch} \, V_{x}^{-}(λ)$ of the level-zero Demazure submodule $V_{x}^{-}(λ)$ over the quantum affine algebra $U_{\mathsf{q}}(\mathfrak{g}_{\mathrm{af}})$ as an explicit finite linear combination of the graded characters of level-zero Demazure submodules. These identities immediately imply the corresponding inverse Chevalley formulas in the torus-equivariant $K$-group of the semi-infinite flag manifold $\mathbf{Q}_{G}$ associated to a connected, simply-connected and simple algebraic group $G$ of type $C$. Also, we derive cancellation-free identities from the identities above of inverse Chevalley type in the case that $μ$ is a standard basis element $\varepsilon_{k}$ in the weight lattice $P$ of $G$.
