Generalized Calogero-Moser systems from rational Cherednik algebras
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Publication:411326
DOI10.1007/s00029-011-0074-yzbMath1243.81089arXiv0809.3487OpenAlexW2163190134MaRDI QIDQ411326
Publication date: 4 April 2012
Published in: Selecta Mathematica. New Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0809.3487
Reflection and Coxeter groups (group-theoretic aspects) (20F55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Groups and algebras in quantum theory and relations with integrable systems (81R12) (n)-body problems (70F10) Integrable cases of motion in rigid body dynamics (70E40) Representation theory of associative rings and algebras (16G99) Root systems (17B22)
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On Cohen-Macaulayness of algebras generated by generalized power sums. With an appendix by Misha Feigin ⋮ Algebra of Dunkl Laplace-Runge-Lenz vector ⋮ Unitary representations of the Cherednik algebra: \(V^*\)-homology ⋮ Deformed Calogero-Moser operators and ideals of rational Cherednik algebras ⋮ Quantum Lax pairs via Dunkl and Cherednik operators ⋮ The quantum harmonic oscillator with icosahedral symmetry and some explicit wavefunctions ⋮ The \(B_2\) harmonic oscillator with reflections and superintegrability ⋮ New orthogonality relations for super-Jack polynomials and an associated Lassalle-Nekrasov correspondence ⋮ Generalized Macdonald-Ruijsenaars systems. ⋮ Jack polynomials as fractional quantum Hall states and the Betti numbers of the \((k+1)\)-equals ideal ⋮ The Dunkl weight function for rational Cherednik algebras ⋮ Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence ⋮ Intertwining operator for AG2 Calogero–Moser–Sutherland system ⋮ Parameters for generalized Hecke algebras in type B ⋮ Trigonometric ∨ -systems and solutions of WDVV equations *
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