论文标题
A型Gaudin代数，RSK和Calogero-Moser细胞
Gaudin Algebras, RSK and Calogero-Moser Cells in Type A
论文作者
论文摘要
我们研究了代数家族，不均匀的高丁代数的频谱，作用于$ n $折叠量表示$ \ Mathbb {c} [x_1，\ ldots，x_r]^{\ otimes^{\ otimes N} $我们使用Halacheva-Kamnitzer-Rybnikov周的工作来证明Robinson-Schensted-Knuth对应关系描述了当我们沿着家族的特殊路径移动时，频谱的行为。我们应用了Mukhin-Tarasov-Varchenko的工作，该作品证明，可以将理性的Calogero-Moser相位空间作为此频谱的一部分实现，以将其与$ T = 0 $ t = 0 $ t = 0 $的行为相关联，$ \ m athfrak {s} _n $ $ \ mathfrak {s} _n $。结果，我们为对称组确认了Bonnafé-Rouquier的猜想，该猜想提出了他们定义的Calogero-Moser细胞与众所周知的Kazhdan-Lusztig细胞之间的平等性。
We study the spectrum of a family of algebras, the inhomogeneous Gaudin algebras, acting on the $n$-fold tensor representation $\mathbb{C}[x_1, \ldots, x_r]^{\otimes n}$ of the Lie algebra $\mathfrak{gl}_r$. We use the work of Halacheva-Kamnitzer-Rybnikov-Weekes to demonstrate that the Robinson-Schensted-Knuth correspondence describes the behaviour of the spectrum as we move along special paths in the family. We apply the work of Mukhin-Tarasov-Varchenko, which proves that the rational Calogero-Moser phase space can be realised as a part of this spectrum, to relate this to behaviour at $t=0$ of rational Cherednik algebras of $\mathfrak{S}_n$. As a result, we confirm for symmetric groups a conjecture of Bonnafé-Rouquier which proposes an equality between the Calogero-Moser cells they defined and the well-known Kazhdan-Lusztig cells.
