论文标题
Yang-baxter方程式用于一般元容器
Yang-Baxter Equations for General Metaplectic Ice
论文作者
论文摘要
在本文中，我们将量子组连接到$ gl_r（f）$的元容器封面的球形惠特克功能扩展到了$ f $ a nonarchimedean本地字段的效果。 Brubaker，Buciumas和Bump表明，对于某些元容器$ n $ fold的封面，$ gl_r（f）$ $ gl_r（f）$一组Yang-baxter方程模型模型标准Intertwiners对主系列惠特克功能的作用。这些方程是由量子仿射的drinfeld扭曲引起的，superalgebra $ u _ {\ sqrt {v}}}（\ wideHat {\ frak {\ frak {gl}}（n）），$ v = q^Q^{ - 1} $ for $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q》。我们将其结果扩展到$ gl_r（f）$的所有Metaplect封面，为Yang-Baxter方程提供了新的解决方案，该方程与相关的Whittaker功能匹配散射矩阵。每个封面都有一个关联的整数不变$ n_q $，并且所得的解决方案连接到量子组$ u _ {\ sqrt {v}}}}（\ wideHat {\ frak {gl}}}（n_q））$ $ u _ {\ sqrt {v}}（\ wideHat {\ frak {gl}}}}（1 | n_q））$。
In this paper, we extend results connecting quantum groups to spherical Whittaker functions on metaplectic covers of $GL_r(F)$, for $F$ a nonarchimedean local field. Brubaker, Buciumas, and Bump showed that for a certain metaplectic $n$-fold cover of $GL_r(F)$ a set of Yang-Baxter equations model the action of standard intertwiners on principal series Whittaker functions. These equations arise from a Drinfeld twist of the quantum affine Lie superalgebra $U_{\sqrt{v}}(\widehat{\frak{gl}}(n)),$ where $v = q^{-1}$ for $q$ the cardinality of the residue field. We extend their results to all metaplectic covers of $GL_r(F)$, providing new solutions to Yang-Baxter equations matching the scattering matrix for the associated Whittaker functions. Each cover has an associated integer invariant $n_Q$ and the resulting solutions are connected to the quantum group $U_{\sqrt{v}}(\widehat{\frak{gl}}(n_Q))$ and quantum superalgebra $U_{\sqrt{v}}(\widehat{\frak{gl}}(1|n_Q))$.
