仿射根系 Macdonald 恒等式与 Nekrasov–Okounkov 型公式的一些组合解释
组合数学
2026-05-18 v2 数学物理
math.MP
表示论
摘要
我们探讨了视为双无穷词的整数的向量与整数分拆之间的一些联系。一方面，该方法使我们能够获得连接钩长乘积与整数向量的计数结果。另一方面，这给出了7个无穷族的仿射根系的 Macdonald 恒等式在 Schur 函数、辛 Schur 函数与特殊正交 Schur 函数方面的组合解释。由这些结果，我们得以导出与每一类型相关的 q-Nekrasov–Okounkov 公式。后者在 q 的极限情形下给出了对应于 Macdonald 所给全部特殊化的 Nekrasov–Okounkov 型公式。
引用
@article{arxiv.2306.08071,
title = {Some combinatorial interpretations of the Macdonald identities for affine root systems and Nekrasov--Okounkov type formulas},
author = {David Wahiche},
journal= {arXiv preprint arXiv:2306.08071},
year = {2026}
}
备注
Major rework. Details have been added. A lot of typos have been now fixed and some of the results in type D were incorrect so it has now been fixed. The organization of the paper has been changed based on recommendations. An interested reader can find a Sagemath version coded by the author to check some of the results of Section 4 and 6