Gaudin algebras, RSK and Calogero-Moser cells in Type A
Gaudin algebras, RSK and Calogero-Moser cells in Type A
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A 型高丁代数、RSK 和 Calogero-Moser 细胞
DOI：
10.1112/plms.12506
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发表时间：
2023
影响因子：
1.8
通讯作者：
Brochier A
中科院分区：
文献类型：
--
作者：
Brochier A
研究了一类代数的谱，即非齐次Gaudin代数，它作用在李代数glr$\mathfrak {gl}_r$的n$n$-重张量表示C[x1，.，xr]<$n${\mathbb{C}}[x_1，\ldots，x_r]^{\otimes n}$上.我们使用的工作Halacheva-Kamnitzer-Rybnikov-Weekes证明，罗宾逊-Schensted-Knuth对应描述的行为的频谱，因为我们移动沿着特殊路径的家庭。我们应用Mukhin-Tarasov-Varchenko的工作，这证明了合理的Calogero-Moser相空间可以实现为这个频谱的一部分，将其与Sn$\mathfrak {S}_n$的有理Cherednik代数在t= 0 $t =0$的行为。因此，我们确认了对称群的Bonnafé-Rouquier猜想，该猜想提出了他们定义的Calogero-Moser胞腔与著名的Kazhdan-Lusztig胞腔之间的相等性。
We study the spectrum of a family of algebras, the inhomogeneous Gaudin algebras, acting on the n$n$‐fold tensor representation C[x1,…,xr]⊗n${\mathbb{C}}[x_1, \ldots , x_r]^{\otimes n}$ of the Lie algebra glr$\mathfrak {gl}_r$. 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$t=0$ of rational Cherednik algebras of Sn$\mathfrak {S}_n$. 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.