论文标题
彩色的骨器模型和基质系数
Colored Bosonic Models and Matrix Coefficients
论文作者
论文摘要
我们开发了有色骨化模型的理论（由Borodin和Wheeler启动）。我们将展示如何使用此类模型的家族来代表$ gl_r（f）$表示的“球形模型”中的iWahori矢量的值，其中$ f $是非一切本的本地字段。我们的结果包括单色分解，这是通过融合更简单的权重来实现玻尔兹曼的权重，将有色模型与未彩色模型相关的局部提升属性，以及offine hecke代数在分区对特定模型家族的分区功能上的作用。作为本地提升属性的应用，我们根据Hall-Littlewood Plynomials评估了Korff定理的Korff定理。我们的结果与代表由Brubaker，Buciumas，Bump和Gustafsson开发的iWahori Whittaker功能的费米子模型的理论非常相似，这两种理论之间具有许多惊人的关系，证明了主要序列表示的球形和惠特克模型的哲学是双重的。
We develop the theory of colored bosonic models (initiated by Borodin and Wheeler). We will show how a family of such models can be used to represent the values of Iwahori vectors in the "spherical model" of representations of $GL_r(F)$, where $F$ is a nonarchimedean local field. Among our results are a monochrome factorization, which is the realization of the Boltzmann weights by fusion of simpler weights, a local lifting property relating the colored models with uncolored models, and an action of the affine Hecke algebra on the partition functions of a particular family of models by Demazure-Lusztig operators. As an application of the local lifting property we reprove a theorem of Korff evaluating the partition functions of the uncolored models in terms of Hall-Littlewood plynomials. Our results are very closely parallel to the theory of fermionic models representing Iwahori Whittaker functions developed by Brubaker, Buciumas, Bump and Gustafsson, with many striking relationships between the two theories, confirming the philosophy that the spherical and Whittaker models of principal series representations are dual.
