论文标题
元容器的Iwahori Whittaker功能和超对称晶格模型
Metaplectic Iwahori Whittaker functions and supersymmetric lattice models
论文作者
论文摘要
在本文中，我们计算$ n $ fold Metaplectic covers $ \ widetilde {g} $ of $ \ mathbf {g} $ of $ \ mathbf {g}（f）$ a $ \ mathbf {g} $，带有$ \ mathbf {g} $ a splitimean local field field field组的新值$ \ widetilde {g} $ of $ \ wideTilde {g} $ of $ n $ fold Metaplede {对于每个IWAHORI WHITTAKER函数$ ϕ $，对于\ widetilde {g} $中的每一个$ g \，我们都会使用小说“向Vector-asazure-whittaker操作员”评估$ ϕ（g）$。一般公式和证明策略的灵感来自于整合系统理论中出现的想法。专门研究$ \ Mathbf {g} = \ MathBf {gl} _r $，我们构建了与量子仿射超级组$ u_q相关的新型的可解决的晶格模型（\ wideHat {\ mathfrak {\ mathfrak {gl}}}}（r | n）（r | n）（r | n）$，并证明其分区$ quals $ $ v）$ c（g）。为了证明这种平等，我们匹配了晶格模型侧（从杨 - 巴克斯特方程获得）上的复发关系与使用$ \ widetilde {g} $的表示理论得出的$ ϕ（g）$的复发关系。值得注意的是，指定分区函数的边界数据与确定Whittaker函数的所有值的数据之间存在培训。
In this paper we compute new values of Iwahori Whittaker functions on $n$-fold metaplectic covers $\widetilde{G}$ of $\mathbf{G}(F)$ with $\mathbf{G}$ a split reductive group over a non-archimedean local field $F$. For every Iwahori Whittaker function $ϕ$, and for every $g\in\widetilde{G}$, we evaluate $ϕ(g)$ by recurrence relations over the Weyl group using novel "vector Demazure-Whittaker operators." The general formula and strategy of proof are inspired by ideas appearing in the theory of integrable systems. Specializing to the case of $\mathbf{G} = \mathbf{GL}_r$, we construct a solvable lattice model of a new type associated with the quantum affine super group $U_q(\widehat{\mathfrak{gl}}(r|n))$ and prove that its partition function equals $ϕ(g)$. To prove this equality we match the recurrence relations on the lattice model side (obtained from the Yang-Baxter equation) to the recurrence relations for $ϕ(g)$ derived by using the representation theory of $\widetilde{G}$. Remarkably, there is a bijection between the boundary data specifying the partition function and the data determining all values of the Whittaker functions.
