An identity in the Bethe subalgebra of C[Sn]$\mathbb {C}[\mathfrak {S}_n]$

DOI10.1112/plms.12560arXiv2207.05743MaRDI QIDQ6139771

Kevin Purbhoo

Publication date: 19 December 2023

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.05743

zbMATH Keywords

Gaudin modelBethe ansatz conjecture

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) PDEs in connection with quantum mechanics (35Q40) Exactly solvable models; Bethe ansatz (82B23) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Classical problems, Schubert calculus (14N15) Fuchsian PDEs (35Q07)

Cites Work

• Bethe subalgebras of the group algebra of the symmetric group
• The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz
• Jeu de taquin and a monodromy problem for Wronskians of polynomials
• A topological proof of the Shapiro-Shapiro conjecture
• Difference operators and duality for trigonometric Gaudin and dynamical Hamiltonians
• Duality for Bethe algebras acting on polynomials in anticommuting variables
• The duality of \(\mathfrak{gl}_{m | n}\) and \(\mathfrak{gl}_k\) Gaudin models
• Wronskians, cyclic group actions, and ribbon tableaux
• An Elementary Proof of the B. and M. Shapiro Conjecture for Rational Functions
• Schubert calculus and representations of the general linear group
• Pole Placement by Static Output Feedback for Generic Linear Systems
• Schubert problems with respect to osculating flags of stable rational curves
• Frontiers of reality in Schubert calculus

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