论文标题
通过具有伪晶体结构的路径模型的对称和非对称麦克唐纳多项式
Symmetric and Nonsymmetric Macdonald Polynomials via a Path Model with a Pseudo-crystal Structure
论文作者
论文摘要
在本文中，我们得出了众所周知的Ram-YIP公式的对应物，用于对称和非对称麦克唐纳的任意类型的多项式。我们的新公式是根据Lakshmibai-Seshadri路径的概括（起源于标准单元理论）的概括，我们称之为pseudo-quantum lakshmibai-shadri（ls）路径。该模型的信息少于壁co在Ram-YIP公式中行走的信息，因此更有效。此外，我们在伪Quantum ls路径上构建了一个连接的伪晶体结构，这有望导致简单的Littlewood-Richardson规则，用于乘以MacDonald多项式。与Kashiwara晶体相反，我们的伪晶体具有任意根标记的边缘。
In this paper we derive a counterpart of the well-known Ram-Yip formula for symmetric and nonsymmetric Macdonald polynomials of arbitrary type. Our new formula is in terms of a generalization of the Lakshmibai-Seshadri paths (originating in standard monomial theory), which we call pseudo-quantum Lakshmibai-Seshadri (LS) paths. This model carries less information than the alcove walks in the Ram-Yip formula, and it is therefore more efficient. Furthermore, we construct a connected pseudo-crystal structure on the pseudo-quantum LS paths, which is expected to lead to a simple Littlewood-Richardson rule for multiplying Macdonald polynomials. By contrast with the Kashiwara crystals, our pseudo-crystals have edges labeled by arbitrary roots.
