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Abstract
We study the spectrum of a family of algebras, the inhomogeneous Gaudin algebras, acting on the nfold tensor representation C[x_1,...,x_r]
n of the Lie algebra gl_r. We use the work of HalachevaKamnitzerRybnikovWeekes to demonstrate that the RobinsonSchenstedKnuth correspondence describes the behaviour of the spectrum as we move along special paths in the family. We apply the work of MukhinTarasovVarchenko, which proves that the rational CalogeroMoser 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 BonnaféRouquier which proposes an equality between the CalogeroMoser cells they defined and the wellknown KazhdanLusztig cells.
n of the Lie algebra gl_r. We use the work of HalachevaKamnitzerRybnikovWeekes to demonstrate that the RobinsonSchenstedKnuth correspondence describes the behaviour of the spectrum as we move along special paths in the family. We apply the work of MukhinTarasovVarchenko, which proves that the rational CalogeroMoser 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 BonnaféRouquier which proposes an equality between the CalogeroMoser cells they defined and the wellknown KazhdanLusztig cells.
Original language  English 

Publisher  ArXiv 
Number of pages  25 
Publication status  Published  18 Dec 2020 
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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

RIGID STRUCTURE IN NONCOMMUTATIVE, GEOMETRIC & COMBINATORIAL PROBLEMS
1/09/08 → 30/06/14
Project: Research
Profiles

Iain Gordon
 College of Science and Engineering  Vice Principal, Head of the College of Sciences and Engineer
 School of Mathematics  Head of School and Chair of Mathematics
Person: Academic: Research Active