Abstract:
We first review the properties of the conventional τ-functions of the KP and Toda-lattice hierarchies. A straightforward generalization is then discussed. It corresponds to passing from differential to finite-difference equations; it does not involve however the concept of operator-valued τ-function nor the one associated with non-Cartanian (level k≠1) algebras. The present study could be useful to understand better q-free fields and their relation to ordinary free fields.
Citation:
A. D. Mironov, A. Yu. Morozov, L. Vinet, “On a c-number quantum τ-function”, TMF, 100:1 (1994), 119–131; Theoret. and Math. Phys., 100:1 (1994), 890–899
This publication is cited in the following 27 articles:
Fei Wang, Min Zhu, Zhaowen Yan, “The Q-deformed SUC, BUC hierarchies and the multi-component generalizations”, Int. J. Geom. Methods Mod. Phys., 21:07 (2024)
A. Mironov, V. Mishnyakov, A. Morozov, “Tau-functions beyond the group elements”, Nuclear Physics B, 1001 (2024), 116504
H. Itoyama, A. Mironov, A. Morozov, “From Kronecker to tableau pseudo-characters in tensor models”, Physics Letters B, 788 (2019), 76
A. Mironov, A. Morozov, Z. Zakirova, “Discrete Painlevé equation, Miwa variables and string equation in 5d matrix models”, J. High Energ. Phys., 2019:10 (2019)
A. Mironov, A. Morozov, A. Sleptsov, “On 6j-symbols for symmetric representations of Uq(suN)”, JETP Letters, 106:10 (2017), 630–636
Melnikov D. Mironov A. Morozov A., “On skew tau-functions in higher spin theory”, J. High Energy Phys., 2016, no. 5, 027
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
A. MIRONOV, A. MOROZOV, SH. SHAKIROV, “TOWARDS A PROOF OF AGT CONJECTURE BY METHODS OF MATRIX MODELS”, Int. J. Mod. Phys. A, 27:01 (2012), 1230001
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
A. Yu. Morozov, “Unitary integrals and related matrix models”, Theoret. and Math. Phys., 162:1 (2010), 1–33
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
Mironov, A, “On AGT relation in the case of U (3)”, Nuclear Physics B, 825:1–2 (2010), 1
Alexandrov, A, “BGWM as second constituent of complex matrix model”, Journal of High Energy Physics, 2009, no. 12, 053
Mironov, A, “Proving AGT relations in the large-c limit”, Physics Letters B, 682:1 (2009), 118
Morozov, A, “ON EQUIVALENCE OF TWO HURWITZ MATRIX MODELS”, Modern Physics Letters A, 24:33 (2009), 2659
Takasaki, K, “Integrable structure of melting crystal model with two q-parameters”, Journal of Geometry and Physics, 59:9 (2009), 1244
Morozov, A, “Generation of matrix models by (W)over-cap-operators”, Journal of High Energy Physics, 2009, no. 4, 064
A. S. Alexandrov, A. D. Mironov, A. Yu. Morozov, “M-Theory of Matrix Models”, Theoret. and Math. Phys., 150:2 (2007), 153–164
Morozov A., “Challenges of matrix models”, String Theory: From Gauge Interactions to Cosmology, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 208, 2006, 129–162
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
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