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This article is cited in 37 scientific papers (total in 37 papers)
Quantum Inverse Scattering Method for the $q$-Boson Model and Symmetric Functions
N. V. Tsilevich
St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
The purpose of this paper is to show that the quantum inverse scattering method for the so-called $q$-boson model has a nice interpretation in terms of the algebra of symmetric functions. In particular, in the case of the
phase model (corresponding to $q=0$) the creation operator coincides (modulo a scalar factor) with the operator of
multiplication by the generating function of complete homogeneous symmetric functions, and the wave functions are expressed via the Schur functions $s_\lambda(x)$. The general case of the $q$-boson model is related in a similar way to the Hall–Littlewood symmetric functions $P_\lambda(x;q^2)$.
Keywords:
$q$-boson model, phase model, quantum inverse scattering method, symmetric functions, Hall–Littlewood functions, Schur functions
DOI:
https://doi.org/10.4213/faa743
 Full text:
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English version:
Functional Analysis and Its Applications, 2006, 40:3, 207–217
Bibliographic databases:
    
UDC:
517.958
Received: 10.08.2005
Citation:
N. V. Tsilevich, “Quantum Inverse Scattering Method for the $q$-Boson Model and Symmetric Functions”, Funktsional. Anal. i Prilozhen., 40:3 (2006), 53–65; Funct. Anal. Appl., 40:3 (2006), 207–217
Citation in format AMSBIB
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N. M. Bogolyubov, “Enumeration of plane partitions and the algebraic Bethe anzatz”, Theoret. and Math. Phys., 150:2 (2007), 165–174
  -
N. M. Bogolyubov, “Four-vertex model”, J. Math. Sci. (N. Y.), 151:2 (2008), 2816–2828
-
N. M. Bogolyubov, “Four-vertex model and random tilings”, Theoret. and Math. Phys., 155:1 (2008), 523–535
-
V. S. Kapitonov, A. G. Pronko, “The five-vertex model and boxed plane partitions”, J. Math. Sci. (N. Y.), 158:6 (2009), 858–867
-
Sulkowski P., “Deformed boson-fermion correspondence, $Q$-bosons, and topological strings on the conifold”, J. High Energy Phys., 2008, no. 10, 104, 17 pp.
-
J. Math. Sci. (N. Y.), 158:6 (2009), 771–786
-
N. M. Bogolyubov, “Five vertex model with fixed boundary conditions”, St. Petersburg Math. J., 21:3 (2010), 407–421
-
Zuparic M., “Phase model expectation values and the 2-Toda hierarchy”, J. Stat. Mech. Theory Exp., 2009, no. 8, P08010, 26 pp.
-
Foda O., Wheeler M., “Hall-Littlewood plane partitions and KP”, Int. Math. Res. Not. IMRN, 2009, no. 14, 2597–2619
-
Nikolay M. Bogolyubov, “Determinantal Representation of the Time-Dependent Stationary Correlation Function for the Totally Asymmetric Simple Exclusion Model”, SIGMA, 5 (2009), 052, 11 pp.
-
Bogoliubov N., Timonen J., “Correlation functions for a strongly coupled boson system and plane partitions”, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 369:1939 (2011), 1319–1333
-
Brubaker B., Bump D., Friedberg S., “Schur polynomials and the Yang–Baxter equation”, Comm. Math. Phys., 308:2 (2011), 281–301
-
Korff Ch., “Cylindric Versions of Specialised Macdonald Functions and a Deformed Verlinde Algebra”, Commun. Math. Phys., 318:1 (2013), 173–246
-
Jan Felipe Van Diejen, Erdal Emsiz, “Boundary Interactions for the Semi-Infinite $q$-Boson System and Hyperoctahedral Hall–Littlewood Polynomials”, SIGMA, 9 (2013), 077, 12 pp.
-
Felipe van Diejen J., Emsiz E., “The Semi-Infinite Q-Boson System with Boundary Interaction”, Lett. Math. Phys., 104:1 (2014), 103–113
-
N. M. Bogolyubov, “Combinatorics of a strongly coupled boson system”, Theoret. and Math. Phys., 181:1 (2014), 1132–1144
-
Motegi K., Sakai K., “K-Theoretic Boson-Fermion Correspondence and Melting Crystals”, J. Phys. A-Math. Theor., 47:44 (2014), 445202
-
Pozsgay B., “Quantum Quenches and Generalized Gibbs Ensemble in a Bethe Ansatz Solvable Lattice Model of Interacting Bosons”, J. Stat. Mech.-Theory Exp., 2014, P10045
-
van Diejen J.F., Emsiz E., “Diagonalization of the Infinite Q-Boson System”, J. Funct. Anal., 266:9 (2014), 5801–5817
-
Borodin A., Corwin I., Petrov L., Sasamoto T., “Spectral Theory For the Q-Boson Particle System”, Compos. Math., 151:1 (2015), 1–67
-
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-
N. M. Bogolyubov, K. L. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70:5 (2015), 789–856
-
J. Math. Sci. (N. Y.), 216:1 (2016), 8–22
-
Cantini L., de Gier J., Wheeler M., “Matrix Product Formula For Macdonald Polynomials”, J. Phys. A-Math. Theor., 48:38 (2015), 384001
-
Betea D., Wheeler M., “Refined Cauchy and Littlewood Identities, Plane Partitions and Symmetry Classes of Alternating Sign Matrices”, J. Comb. Theory Ser. A, 137 (2016), 126–165
-
J. Math. Sci. (N. Y.), 224:2 (2017), 199–213
-
Wheeler M., Zinn-Justin P., “Refined Cauchy/Littlewood identities and six-vertex model partition functions: III. Deformed bosons”, Adv. Math., 299 (2016), 543–600
-
Duval A., Pasquier V., “q -bosons, Toda lattice, Pieri rules and Baxter q -operator”, J. Phys. A-Math. Theor., 49:15 (2016), 154006
-
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-
Motegi K., “Combinatorial Properties of Symmetric Polynomials From Integrable Vertex Models in Finite Lattice”, J. Math. Phys., 58:9 (2017), 091703
-
Wang N., Wu K., “Vertex Operators, T-Boson Model and Weighted Plane Partitions in Finite Boxes”, Mod. Phys. Lett. B, 32:5 (2018), 1850061
-
Felipe van Diejen J., Emsiz E., Nahuel Zurrian I., “Completeness of the Bethe Ansatz For An Open -Boson System With Integrable Boundary Interactions”, Ann. Henri Poincare, 19:5 (2018), 1349–1384
-
Bogoliubov N., Malyshev C., “The Phase Model and the Norm-Trace Generating Function of Plane Partitions”, J. Stat. Mech.-Theory Exp., 2018, 083101
-
Wheeler M., Zinn-Justin P., “Hall Polynomials, Inverse Kostka Polynomials and Puzzles”, J. Comb. Theory Ser. A, 159 (2018), 107–163
-
Barraquand G., Borodin A., Corwin I., Wheeler M., “Stochastic Six-Vertex Model in a Half-Quadrant and Half-Line Open Asymmetric Simple Exclusion Process”, Duke Math. J., 167:13 (2018), 2457–2529
-
Wang N., “Young Diagrams in An N X M Box and the Kp Hierarchy”, Nucl. Phys. B, 937 (2018), 478–501
-
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