Operator calculi associated with reflection groups

DOI10.1215/S0012-7094-87-05501-3zbMath0629.57027OpenAlexW1993408855MaRDI QIDQ1093960

Eugene Gutkin

Publication date: 1987

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-87-05501-3

zbMATH Keywords

Weyl groupfinite difference operatorssemisimple Lie groupquantum HamiltoniansBethe Ansatzsimple reflectionsreflection groups on manifoldsEuclidean reflection groupsSchubert calculus on flag varieties

Mathematics Subject Classification ID

Transformation groups and semigroups (topological aspects) (54H15) Other geometric groups, including crystallographic groups (20H15) Discontinuous groups of transformations (57S30) Applications of linear algebraic groups to the sciences (20G45)

Related Items

Periodic integrable systems with delta-potentials, Bethe Ansatz and the generalized Yang-Baxter equations, Representations of Hecke Algebras

Cites Work

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• Groups generated by reflections and aspherical manifolds not covered by Euclidean space
• Infinite dimensional Lie algebras. An introduction
• Integrable systems with Delta-potential
• Geometry and combinatorics of groups generated by reflections
• Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction