Representation theoretic interpretation and interpolation properties of inhomogeneous spin q-Whittaker polynomials

Selecta Mathematica Pub Date : 2024-04-02 DOI:10.1007/s00029-024-00930-w

引用次数: 0

Abstract

We establish new properties of inhomogeneous spin q-Whittaker polynomials, which are symmetric polynomials generalizing $t=0$ Macdonald polynomials. We show that these polynomials are defined in terms of a vertex model, whose weights come not from an R-matrix, as is often the case, but from other intertwining operators of $U'_q({\widehat{\mathfrak {sl}}}_2)$ -modules. Using this construction, we are able to prove a Cauchy-type identity for inhomogeneous spin q-Whittaker polynomials in full generality. Moreover, we are able to characterize spin q-Whittaker polynomials in terms of vanishing at certain points, and we find interpolation analogues of q-Whittaker and elementary symmetric polynomials.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

非均质自旋 q-Whittaker 多项式的表示论解释和插值特性

摘要我们建立了非均质自旋 q-Whittaker 多项式的新性质，它们是对称多项式对 $t=0$ Macdonald 多项式的概括。我们证明这些多项式是根据顶点模型定义的，其权重不是像通常那样来自 R 矩阵，而是来自 $U'_q({\widehat{\mathfrak {sl}}_2)$ 的其他交织算子。）-模块。利用这种构造，我们能够证明非均质自旋 q-Whittaker 多项式的一个完全通用的 Cauchy-type 特性。此外，我们还能用在某些点上的消失来描述自旋 q-Whittaker 多项式的特征，并找到 q-Whittaker 多项式和基本对称多项式的插值类比。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Selecta Mathematica

自引率

0.00%

发文量

期刊最新文献

Parabolic recursions for Kazhdan–Lusztig polynomials and the hypercube decomposition Tomographic Fourier extension identities for submanifolds of $${\mathbb {R}}^n$$ The Morrison–Kawamata cone conjecture for singular symplectic varieties Colored vertex models and Iwahori Whittaker functions The module structure of a group action on a ring