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TMF, 1998, Volume 114, Number 2, Pages 163–232 (Mi tmf836)  

This article is cited in 37 scientific papers (total in 37 papers)

Group theory approach to the $\tau$-function and its quantization

A. D. Mironov

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: This is a review of generalizations of the $\tau$-function and integrable hierarchies and of their group theory interpretations, which admits an immediate quantization procedure. Different group theory structures related to the integrable system, as well as their quantum deformations, are discussed.


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Theoretical and Mathematical Physics, 1998, 114:2, 127–183

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Received: 13.10.1997

Citation: A. D. Mironov, “Group theory approach to the $\tau$-function and its quantization”, TMF, 114:2 (1998), 163–232; Theoret. and Math. Phys., 114:2 (1998), 127–183

Citation in format AMSBIB
\by A.~D.~Mironov
\paper Group theory approach to the $\tau$-function and its quantization
\jour TMF
\yr 1998
\vol 114
\issue 2
\pages 163--232
\jour Theoret. and Math. Phys.
\yr 1998
\vol 114
\issue 2
\pages 127--183

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    This publication is cited in the following articles:
    1. Mironov, A, “Commuting Hamiltonians from Seiberg-Witten Theta-functions”, Physics Letters B, 475:1–2 (2000), 71  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    2. Orlov, AY, “Milne's hypergeometric functions in terms of free fermions”, Journal of Physics A-Mathematical and General, 34:11 (2001), 2295  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. Mironov, A, “p, q-duality and Hamiltonian flows in the space of integrable systems or integrable systems as canonical transforms”, Physics Letters B, 524:1–2 (2002), 217  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. Itoyama, H, “The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory”, Nuclear Physics B, 657:1–3 (2003), 53  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    5. Alexandrov A, Morozov A, Mironov A, “Partition functions of matrix models: First special functions of string theory”, International Journal of Modern Physics A, 19:24 (2004), 4127–4163  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    6. A. S. Alexandrov, A. D. Mironov, A. Yu. Morozov, “Partition functions of matrix models as the first special functions of string theory: Finite Hermitian one-matrix model”, Theoret. and Math. Phys., 142:3 (2005), 349–411  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. A. S. Alexandrov, A. D. Mironov, A. Yu. Morozov, “$M$-Theory of Matrix Models”, Theoret. and Math. Phys., 150:2 (2007), 153–164  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. Alexandrov, A, “BGWM as second constituent of complex matrix model”, Journal of High Energy Physics, 2009, no. 12, 053  crossref  mathscinet  isi  scopus  scopus  scopus
    9. Mironov, A, “Proving AGT relations in the large-c limit”, Physics Letters B, 682:1 (2009), 118  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus  scopus
    10. A. Yu. Morozov, “Unitary integrals and related matrix models”, Theoret. and Math. Phys., 162:1 (2010), 1–33  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. Mironov, A, “Linearized Lorentz-violating gravity and discriminant locus in the moduli space of mass terms”, Journal of Physics A-Mathematical and Theoretical, 43:5 (2010), 055402  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    12. Mironov, A, “On AGT relation in the case of U (3)”, Nuclear Physics B, 825:1–2 (2010), 1  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    13. Mironov A., Morozov A., Shakirov Sh., “Matrix model conjecture for exact BS periods and Nekrasov functions”, Journal of High Energy Physics, 2010, no. 2, 030  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    14. Mironov A., Morozov A., Shakirov Sh., “Conformal Blocks as Dotsenko-Fateev Integral Discriminants”, Internat J Modern Phys A, 25:16 (2010), 3173–3207  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    15. Mironov A., Morozov A., “Nekrasov functions from exact Bohr-Sommerfeld periods: the case of SU(N)”, J. Phys. A: Math. Theor., 43:19 (2010), 195401  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    16. A. D. Mironov, A. Yu. Morozov, S. M. Natanzon, “Complete set of cut-and-join operators in the Hurwitz–Kontsevich theory”, Theoret. and Math. Phys., 166:1 (2011), 1–22  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    17. Alexandrov A., Mironov A., Morozov A., Natanzon S., “Integrability of Hurwitz partition functions”, J. Phys. A: Math. Theor., 45:4 (2012), 045209  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    18. Mironov A., Morozov A., Shakirov Sh., “Towards a Proof of AGT Conjecture By Methods of Matrix Models”, Internat J Modern Phys A, 27:1 (2012), 1230001  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    19. D. V. Galakhov, A. D. Mironov, A. Yu. Morozov, A. V. Smirnov, “Three-dimensional extensions of the Alday–Gaiotto–Tachikawa relation”, Theoret. and Math. Phys., 172:1 (2012), 939–962  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    20. JETP Letters, 95:11 (2012), 586–593  mathnet  crossref  isi  elib  elib
    21. A. Yu. Morozov, “Challenges of $\beta$-deformation”, Theoret. and Math. Phys., 173:1 (2012), 1417–1437  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    22. Mironov A. Morozov A., “Equations on Knot Polynomials and 3D/5D Duality”, Sixth International School on Field Theory and Gravitation-2012, AIP Conference Proceedings, 1483, ed. Rodrigues W. Kerner R. Pires G. Pinheiro C., Amer Inst Physics, 2012, 189–211  crossref  adsnasa  isi  scopus  scopus  scopus
    23. Mironov A. Morozov A. Shakirov Sh., “Torus Homflypt as the Hall-Littlewood Polynomials”, J. Phys. A-Math. Theor., 45:35 (2012), 355202  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    24. Mironov A. Morozov A. Zakirova Z., “Comment on Integrability in Dijkgraaf-Vafa Beta-Ensembles”, Phys. Lett. B, 711:3-4 (2012), 332–335  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus  scopus
    25. Mironov A. Morozov A. Sleptsov A., “On Genus Expansion of Knot Polynomials and Hidden Structure of Hurwitz Tau-Functions”, Eur. Phys. J. C, 73:7 (2013), 2492  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    26. Anokhina A., Mironov A., Morozov A., Morozov A., “Colored Homfly Polynomials as Multiple Sums Over Paths Or Standard Young Tableaux”, Adv. High. Energy Phys., 2013, 931830  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    27. A. V. Popolitov, “Relation between Nekrasov functions and Bohr–Sommerfeld periods in the pure $SU(N)$ case”, Theoret. and Math. Phys., 178:2 (2014), 239–252  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    28. JETP Letters, 100:4 (2014), 271–278  mathnet  crossref  crossref  isi  elib  elib
    29. Nieri F. Pasquetti S. Passerini F. Torrielli A., “5D Partition Functions, Q-Virasoro Systems and Integrable Spin-Chains”, J. High Energy Phys., 2014, no. 12, 040  crossref  isi  scopus  scopus  scopus
    30. Sleptsov A., “Hidden Structures of Knot Invariants”, Int. J. Mod. Phys. A, 29:29 (2014), 1430063  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    31. Alexandrov A. Mironov A. Morozov A. Natanzon S., “On KP-Integrable Hurwitz Functions”, J. High Energy Phys., 2014, no. 11, 080  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    32. H. Itoyama, A. D. Mironov, A. Yu. Morozov, “Matching branches of a nonperturbative conformal block at its singularity divisor”, Theoret. and Math. Phys., 184:1 (2015), 891–923  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    33. Morozov A., Zenkevich Y., “Decomposing Nekrasov Decomposition”, J. High Energy Phys., 2016, no. 2, 098  crossref  mathscinet  isi  scopus  scopus  scopus
    34. Awata H., Kanno H., Mironov A., Morozov A., Morozov A., Ohkubo Yu., Zenkevich Y., “Toric Calabi-Yau threefolds as quantum integrable systems.
      $$ \mathrm{\mathcal{R}} $$
      -matrix and T T
      $$ \mathrm{\mathcal{R}}\mathcal{T}\mathcal{T} $$
      relations”, J. High Energy Phys., 2016, no. 10, 047  crossref  mathscinet  isi  elib  scopus
    35. Melnikov D. Mironov A. Morozov A., “On skew tau-functions in higher spin theory”, J. High Energy Phys., 2016, no. 5, 027  crossref  mathscinet  isi  elib  scopus
    36. Awata H., Kanno H., Mironov A., Morozov A., Morozov A., Ohkubo Yu., Zenkevich Y., “Anomaly in RTT relation for DIM algebra and network matrix models”, Nucl. Phys. B, 918 (2017), 358–385  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    37. Itoyama H. Mironov A. Morozov A., “From Kronecker to Tableau Pseudo-Characters in Tensor Models”, Phys. Lett. B, 788 (2019), 76–81  crossref  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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