General information
Latest issue
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS


Personal entry:
Save password
Forgotten password?

TMF, 1984, Volume 61, Number 1, Pages 35–44 (Mi tmf5654)  

This article is cited in 56 scientific papers (total in 56 papers)

Factorizing particles on a half-line and root systems

I. V. Cherednik

Abstract: Factorization conditions are obtained and an example is given of a theory of equal-mass relativistic particles on a half-line with reflection corresponding to the $B_n$, $C_n$, $D_n$ root systems. Generalized factorization equations are introduced, and the analog of Yang's $S$ matrix is considered for an arbitrary root system. For the system $B_n$ an example of an $S$ matrix with elliptic dependence on the rapidities is constructed; it generalizes Belavin's $S$ matrix.

Full text: PDF file (1195 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 1984, 61:1, 977–983

Bibliographic databases:

Received: 01.12.1983

Citation: I. V. Cherednik, “Factorizing particles on a half-line and root systems”, TMF, 61:1 (1984), 35–44; Theoret. and Math. Phys., 61:1 (1984), 977–983

Citation in format AMSBIB
\by I.~V.~Cherednik
\paper Factorizing particles on a half-line and root systems
\jour TMF
\yr 1984
\vol 61
\issue 1
\pages 35--44
\jour Theoret. and Math. Phys.
\yr 1984
\vol 61
\issue 1
\pages 977--983

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. P. Zhelobenko, “Extremal-type equations and their resolvents over reductive Lie algebras”, Funct. Anal. Appl., 19:4 (1985), 325–327  mathnet  crossref  mathscinet  zmath  isi
    2. I. V. Cherednik, “Special bases of irreducible representations of a degenerate affine Hecke algebra”, Funct. Anal. Appl., 20:1 (1986), 76–78  mathnet  crossref  mathscinet  zmath  isi
    3. Yu. I. Manin, V. V. Schechtman, “Higher Bruhat orders, related to the symmetric group”, Funct. Anal. Appl., 20:2 (1986), 148–150  mathnet  crossref  mathscinet  zmath  isi
    4. E. K. Sklyanin, “Boundary conditions for integrable equations”, Funct. Anal. Appl., 21:2 (1987), 164–166  mathnet  crossref  mathscinet  zmath  isi
    5. D. P. Zhelobenko, “Extremal cocycles of Weyl groups”, Funct. Anal. Appl., 21:3 (1987), 183–192  mathnet  crossref  mathscinet  zmath  isi
    6. V. L. Bulatov, “Ground state and excitations of a one-dimensional bose gas on a finite interval”, Theoret. and Math. Phys., 75:1 (1988), 433–439  mathnet  crossref  mathscinet  isi
    7. Theoret. and Math. Phys., 104:1 (1995), 762–776  mathnet  crossref  mathscinet  zmath  isi
    8. A. I. Molev, M. L. Nazarov, G. I. Olshanskii, “Yangians and classical Lie algebras”, Russian Math. Surveys, 51:2 (1996), 205–282  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. D. I. Gurevich, P. A. Saponov, “Higher-Dimensional Representations of the Reflection Equation Algebra”, Theoret. and Math. Phys., 139:1 (2004), 486–499  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    10. Tsiganov, AV, “Integrable systems on so(4) related to XXX spin chains with boundaries”, Journal of Physics A-Mathematical and General, 37:17 (2004), 4843  crossref  isi
    11. N. J. MacKay, “Boundary integrability of nonlinear sigma models”, Theoret. and Math. Phys., 142:2 (2005), 270–274  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. Mackay, NJ, “Introduction to Yangian symmetry in integrable field theory”, International Journal of Modern Physics A, 20:30 (2005), 7189  crossref  isi
    13. Doikou, A, “From affine Hecke algebras to boundary symmetries”, Nuclear Physics B, 725:3 (2005), 493  crossref  isi
    14. Baseilhac, P, “A new (in)finite-dimensional algebra for quantum integrable models”, Nuclear Physics B, 720:3 (2005), 325  crossref  isi
    15. Baseilhac, P, “Deformed Dolan-Grady relations in quantum integrable models”, Nuclear Physics B, 709:3 (2005), 491  crossref  isi
    16. Arnaudon, D, “Analytical Bethe ansatz for closed and open gl(N)-spin chains in any representation”, Journal of Statistical Mechanics-Theory and Experiment, 2005, P02007  isi
    17. Doikou, A, “The open XXZ and associated models at q root of unity”, Journal of Statistical Mechanics-Theory and Experiment, 2006, P09010  isi
    18. Nichols, A, “The Temperley-Lieb algebra and its generalizations in the Potts and XXZ models”, Journal of Statistical Mechanics-Theory and Experiment, 2006, P01003  isi
    19. H. Frahm, G. Palacios, “Integrable Anderson-type impurity in the supersymmetric $t$$J$ model”, Theoret. and Math. Phys., 150:2 (2007), 288–300  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. Doikou, A, “A note on the boundary spin s XXZ chain”, Physics Letters A, 366:6 (2007), 556  crossref  isi
    21. Anastasia Doikou, “Asymmetric Twin Representation: the Transfer Matrix Symmetry”, SIGMA, 3 (2007), 009, 19 pp.  mathnet  crossref  mathscinet  zmath
    22. D. I. Gurevich, P. N. Pyatov, P. A. Saponov, “Representation theory of (modified) Reflection Equation Algebra of $GL(m|n)$ type”, St. Petersburg Math. J., 20:2 (2009), 213–253  mathnet  crossref  mathscinet  zmath  isi
    23. Ivan Cherednik, Keith Schneider, “Non-Gatherable Triples for Non-Affine Root Systems”, SIGMA, 4 (2008), 079, 12 pp.  mathnet  crossref  mathscinet  zmath
    24. Belliard, S, “The nested Bethe ansatz for 'all' open spin chains with diagonal boundary conditions”, Journal of Physics A-Mathematical and Theoretical, 42:20 (2009), 205203  crossref  zmath  adsnasa  isi
    25. Gurevich, D, “Braided affine geometry and q-analogs of wave operators”, Journal of Physics A-Mathematical and Theoretical, 42:31 (2009), 313001  crossref  isi
    26. P. P. Kulish, N. Manoilovich, Z. Nagy, “Jordanian deformation of the open XXX spin chain”, Theoret. and Math. Phys., 163:2 (2010), 644–652  mathnet  crossref  crossref  adsnasa  isi  elib
    27. Anastasia Doikou, Nikos Karaiskos, “Junction Type Representations of the Temperley–Lieb Algebra and Associated Symmetries”, SIGMA, 6 (2010), 089, 19 pp.  mathnet  crossref  mathscinet
    28. F. Alberto Grünbaum, Mizan Rahman, “On a Family of $2$-Variable Orthogonal Krawtchouk Polynomials”, SIGMA, 6 (2010), 090, 12 pp.  mathnet  crossref  mathscinet
    29. Gurevich D., Saponov P., “Generic super-orbits in gl(m vertical bar n)* and their braided counterparts”, J Geom Phys, 60:10 (2010), 1411–1423  crossref  isi
    30. Ghali Filali, Nikolai Kitanine, “Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End”, SIGMA, 7 (2011), 012, 22 pp.  mathnet  crossref  mathscinet
    31. Baseilhac P., Belliard S., “The central extension of the reflection equations and an analog of Miki's formula”, J. Phys. A: Math. Theor., 44:41 (2011), 415205  crossref  isi
    32. D. V. Artamonov, V. A. Golubeva, “Noncommutative Pfaffians associated with the orthogonal algebra”, Sb. Math., 203:12 (2012), 1685–1714  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    33. Khoroshkin S., Nazarov M., “Mickelsson Algebras and Representations of Yangians”, Trans. Am. Math. Soc., 364:3 (2012), 1293–1367  isi
    34. Kuniba A., Okado M., “Tetrahedron and 3D Reflection Equations From Quantized Algebra of Functions”, J. Phys. A-Math. Theor., 45:46 (2012), 465206  crossref  isi
    35. Corrigan E., Zambon C., “Infinite Dimension Reflection Matrices in the sine-Gordon Model with a Boundary”, J. High Energy Phys., 2012, no. 6, 050  crossref  isi
    36. Samuel Belliard, Nicolas Crampé, “Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz”, SIGMA, 9 (2013), 072, 12 pp.  mathnet  crossref  mathscinet
    37. Caudrelier V., Crampe N., Zhang Q.C., “Set-Theoretical Reflection Equation: Classification of Reflection Maps”, J. Phys. A-Math. Theor., 46:9 (2013), 095203  crossref  isi
    38. Ribeiro G.A.P. Lima-Santos A., “Bethe Ansatz for the Temperley-Lieb Spin Chain with Integrable Open Boundaries”, J. Stat. Mech.-Theory Exp., 2013, P02035  crossref  isi
    39. Lima-Santos A., “Temperley-Lieb K-Matrices”, J. Stat. Mech.-Theory Exp., 2013, P10021  crossref  isi
    40. Antonio N.C., Manojlovic N., Nagy Z., “Trigonometric Sl (2) Gaudin Model with Boundary Terms”, Rev. Math. Phys., 25:10, SI (2013), 1343004  crossref  isi
    41. Vincent Caudrelier, Nicolas Crampé, Qi Cheng Zhang, “Integrable Boundary for Quad-Graph Systems: Three-Dimensional Boundary Consistency”, SIGMA, 10 (2014), 014, 24 pp.  mathnet  crossref  mathscinet
    42. N. Cirilo Antonio, N. Manoilovich, Z. Nagy, “Jordanian deformation of the open $s\ell(2)$ Gaudin model”, Theoret. and Math. Phys., 179:1 (2014), 462–471  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
    43. Babichenko A., Regelskis V., “On Boundary Fusion and Functional Relations in the Baxterized Affine Hecke Algebra”, J. Math. Phys., 55:4 (2014), 043503  crossref  isi
    44. Ribeiro G.A.P., Korepin V.E., “Thermodynamic Limit of the Six-Vertex Model With Reflecting End”, J. Phys. A-Math. Theor., 48:4 (2015), 045205  crossref  isi
    45. Grosjean N. Maillet J.-M. Niccoli G., “On the Form Factors of Local Operators in the Bazhanov-Stroganov and Chiral Potts Models”, Ann. Henri Poincare, 16:5 (2015), 1103–1153  crossref  isi
    46. Aristophanes Dimakis, Folkert Müller-Hoissen, “Simplex and Polygon Equations”, SIGMA, 11 (2015), 042, 49 pp.  mathnet  crossref  mathscinet
    47. Lima-Santos A., “On the
      U q [ o s p ( 1 | 2 ) ] Temperley?Lieb Model”, J. Stat. Phys., 165:5 (2016), 953–969  crossref  mathscinet  zmath  isi  elib  scopus
    48. Samuel Belliard, Vidas Regelskis, “Drinfeld J Presentation of Twisted Yangians”, SIGMA, 13 (2017), 011, 35 pp.  mathnet  crossref
    49. Fioravanti D., Nepomechie R.L., “An inhomogeneous Lax representation for the Hirota equation”, J. Phys. A-Math. Theor., 50:5 (2017), 054001  crossref  mathscinet  zmath  isi  scopus
    50. O. V. Ogievetskii, B. Herlemont, “Rings of $\mathbf h$-deformed differential operators”, Theoret. and Math. Phys., 192:2 (2017), 1218–1229  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    51. Ahmed I., Nepomechie R.I., Wang Ch., “Quantum Group Symmetries and Completeness For a(2N)((2)) Open Spin Chains”, J. Phys. A-Math. Theor., 50:28 (2017), 284002  crossref  isi
    52. Hadjiivanov L., Furlan P., “Quantum Groups as Generalized Gauge Symmetries in WZNW Models. Part II. the Quantized Model”, Phys. Part. Nuclei, 48:4 (2017), 564–621  crossref  isi
    53. Gerdjikov V.S., Grahovski G.G., Ivanov R.I., “On Integrable Wave Interactions and Lax pairs on Symmetric Spaces”, Wave Motion, 71:SI (2017), 53–70  crossref  isi
    54. Behrend R.E., Fischer I., Konvalinka M., “Diagonally and Antidiagonally Symmetric Alternating Sign Matrices of Odd Order”, Adv. Math., 315 (2017), 324–365  crossref  isi
    55. Jules Lamers, “The Functional Method for the Domain-Wall Partition Function”, SIGMA, 14 (2018), 064, 23 pp.  mathnet  crossref
    56. Li Y., “Quiver Varieties and Symmetric Pairs”, Represent. Theory, 23 (2019), 1–56  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:467
    Full text:203
    First page:1

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019