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Abstract / Description of output
We study the spectrum of a family of algebras, the inhomogeneous Gaudin algebras, acting on the n-fold tensor representation C[x_1,...,x_r]
n of the Lie algebra 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 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.
n of the Lie algebra 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 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.
Original language | English |
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Pages (from-to) | 1467-1495 |
Number of pages | 25 |
Journal | Proceedings of the London Mathematical Society |
Volume | 126 |
Issue number | 5 |
Early online date | 4 Apr 2023 |
DOIs | |
Publication status | Published - 31 May 2023 |
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Dive into the research topics of 'Gaudin Algebras, RSK and Calogero-Moser cells in type A'. Together they form a unique fingerprint.Projects
- 2 Finished
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Enhancing Representation Theory, Noncommutative Algebra And Geometry Through Moduli, Stability And Deformations
Gordon, I., Bayer, A. & Smoktunowicz, A.
1/05/18 → 30/04/24
Project: Research
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RIGID STRUCTURE IN NONCOMMUTATIVE, GEOMETRIC & COMBINATORIAL PROBLEMS
1/09/08 → 30/06/14
Project: Research
Profiles
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Iain Gordon
- College of Science and Engineering - Vice Principal, Head of the College of Sciences and Engineer
Person: Academic: Research Active