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Uspekhi Mat. Nauk, 1996, Volume 51, Issue 3(309), Pages 185–186 (Mi umn976)  

This article is cited in 41 scientific papers (total in 42 papers)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

New integrable deformations of the Calogero–Moser quantum problem

A. P. Veselov, M. V. Feigin, O. A. Chalykh

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

DOI: https://doi.org/10.4213/rm976

Full text: PDF file (237 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1996, 51:3, 573–574

Bibliographic databases:

MSC: 34L40, 20F55, 35Lxx
Accepted: 07.05.1996

Citation: A. P. Veselov, M. V. Feigin, O. A. Chalykh, “New integrable deformations of the Calogero–Moser quantum problem”, Uspekhi Mat. Nauk, 51:3(309) (1996), 185–186; Russian Math. Surveys, 51:3 (1996), 573–574

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. A. Chalykh, “The duality of the generalized Calogero and Ruijsenaars problems”, Russian Math. Surveys, 52:6 (1997), 1289–1291  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Berest, YY, “Huygens' principle in Minkowski spaces and soliton solutions of the Korteweg-de Vries equation”, Communications in Mathematical Physics, 190:1 (1997), 113  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    3. Yu. Yu. Berest, A. P. Veselov, “On the singularities of potentials of exactly soluble Schrödinger equations and on Hadamard's problem”, Russian Math. Surveys, 53:1 (1998), 208–209  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. O. A. Chalykh, “Darboux transformations for multidimensional Schrödinger operators”, Russian Math. Surveys, 53:2 (1998), 377–379  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Berest, Y, “Hierarchies of Huygens' operators and Hadamard's conjecture”, Acta Applicandae Mathematicae, 53:2 (1998), 125  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. Hietarinta, J, “Pure quantum integrability”, Physics Letters A, 246:1–2 (1998), 97  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    7. Okounkov, A, “On Newton interpolation of symmetric functions: A characterization of interpolation Macdonald polynomials”, Advances in Applied Mathematics, 20:4 (1998), 395  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    8. Berest, Y, “D-modules and Darboux transformations”, Letters in Mathematical Physics, 43:3 (1998), 279  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Chalykh, O, “New integrable generalizations of Calogero–Moser quantum problem”, Journal of Mathematical Physics, 39:2 (1998), 695  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    10. Chalykh, OA, “Multidimensional Baker-Akhiezer functions and Huygens' principle”, Communications in Mathematical Physics, 206:3 (1999), 533  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    11. Veselov, AP, “Deformations of the root systems and new solutions to generalised WDVV equations”, Physics Letters A, 261:5–6 (1999), 297  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    12. Chalykh, OA, “Multidimensional integrable Schrodinger operators with matrix potential”, Journal of Mathematical Physics, 40:11 (1999), 5341  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    13. Oleg A. Chalykh, “Bispectrality for the quantum Ruijsenaars model and its integrable deformation”, J Math Phys (N Y ), 41:8 (2000), 5139  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    14. Twarock, R, “An exactly solvable Calogero model for a non-integrally laced group”, Physics Letters A, 275:3 (2000), 169  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    15. Berest, Y, “On the structure of singularities of integrable Schrodinger operators”, Letters in Mathematical Physics, 52:2 (2000), 103  crossref  mathscinet  zmath  isi  scopus  scopus
    16. Berest, Y, “The problem of lacunas and analysis on root systems”, Transactions of the American Mathematical Society, 352:8 (2000), 3743  crossref  mathscinet  zmath  isi
    17. Chalykh, OA, “Harmonic oscillator and Darboux transformations in many dimensions”, Physics Letters A, 267:4 (2000), 256  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    18. Veselov A.P., “On geometry of a special class of solutions to generalized WDVV equations”, Integrability: the Seiberg-Witten and Whitham Equations, 2000, 125–135  mathscinet  zmath  isi
    19. Chalykh, OA, “Locus configurations and boolean OR-systems”, Physics Letters A, 285:5–6 (2001), 339  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    20. Khodarinova, LA, “On algebraic integrability of the deformed elliptic Calogero–Moser problem”, Journal of Nonlinear Mathematical Physics, 8:1 (2001), 50  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    21. Sergeev, A, “Superanalogs of the Calogero operators and Jack polynomials”, Journal of Nonlinear Mathematical Physics, 8:1 (2001), 59  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    22. A. N. Sergeev, “Calogero Operator and Lie Superalgebras”, Theoret. and Math. Phys., 131:3 (2002), 747–764  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    23. Veselov, AP, “On generalizations of the Calogero–Moser-Sutherland quantum problem and WDVV equations”, Journal of Mathematical Physics, 43:11 (2002), 5675  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    24. Chalykh, OA, “Macdonald polynomials and algebraic integrability”, Advances in Mathematics, 166:2 (2002), 193  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    25. Feigin, M, “Quasi-invariants of Coxeter groups and m-harmonic polynomials”, International Mathematics Research Notices, 2002, no. 10, 521  crossref  mathscinet  zmath  isi  elib
    26. Feigin, M, “Quasi-invariants and quantum integrals of the deformed Calogero–Moser systems”, International Mathematics Research Notices, 2003, no. 46, 2487  crossref  mathscinet  zmath  isi  elib
    27. Veselov, AP, “Yang–Baxter maps and integrable dynamics”, Physics Letters A, 314:3 (2003), 214  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    28. Taniguchi, K, “On the symmetry of commuting differential operators with sinpularities along hyperplanes”, International Mathematics Research Notices, 2004, no. 36, 1845  crossref  mathscinet  zmath  isi
    29. Sergeev, AN, “Deformed quantum Calogero–Moser problems and Lie superalgebras”, Communications in Mathematical Physics, 245:2 (2004), 249  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    30. Feigin, M, “Bispectrality for deformed Calogero–Moser-Sutherland systems”, Journal of Nonlinear Mathematical Physics, 12 (2005), 95  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    31. Sergeev, A, “Generalised discriminants, deformed Calogero–Moser-Sutherland operators and super-Jack polynomials”, Advances in Mathematics, 192:2 (2005), 341  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    32. Khodarinova, LA, “Quantum integrability of the deformed elliptic Calogero–Moser problem”, Journal of Mathematical Physics, 46:3 (2005), 033506  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    33. Feigin, MV, “Logarithmic Frobenius structures and Coxeter discriminants”, Advances in Mathematics, 212:1 (2007), 143  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    34. Chalykh, O, “Algebro-geometric Schrodinger operators in many dimensions”, Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 366:1867 (2008), 947  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    35. Previato, E, “Multivariable Burchnall-Chaundy theory”, Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 366:1867 (2008), 1155  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    36. Sergeev, AN, “Deformed Macdonald-Ruijsenaars Operators and Super Macdonald Polynomials”, Communications in Mathematical Physics, 288:2 (2009), 653  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    37. Felder, G, “BAKER-AKHIEZER FUNCTION AS ITERATED RESIDUE AND SELBERG-TYPE INTEGRAL”, Glasgow Mathematical Journal, 51A (2009), 59  crossref  mathscinet  zmath  isi  scopus  scopus
    38. A. B. Zheglov, A. E. Mironov, “Moduli Beikera – Akhiezera, puchki Krichevera i kommutativnye koltsa differentsialnykh operatorov v chastnykh proizvodnykh”, Dalnevost. matem. zhurn., 12:1 (2012), 20–34  mathnet
    39. Feigin M., “Generalized Calogero–Moser Systems From Rational Cherednik Algebras”, Sel. Math.-New Ser., 18:1 (2012), 253–281  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    40. M. V. Feigin, M. A. Hallnäs, A. P. Veselov, “Baker-Akhiezer functions and generalised Macdonald-Mehta integrals”, J. Math. Phys, 54:5 (2013), 052106  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    41. Feigin M. Johnston D., “A Class of Baker-Akhiezer Arrangements”, Commun. Math. Phys., 328:3 (2014), 1117–1157  crossref  mathscinet  zmath  isi  scopus  scopus
    42. V. E. Adler, Yu. Yu. Berest, V. M. Buchstaber, P. G. Grinevich, B. A. Dubrovin, I. M. Krichever, S. P. Novikov, A. N. Sergeev, M. V. Feigin, J. Felder, E. V. Ferapontov, O. A. Chalykh, P. I. Etingof, “Alexander Petrovich Veselov (on his 60th birthday)”, Russian Math. Surveys, 71:6 (2016), 1159–1176  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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