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

Funktsional'nyi Analiz i ego Prilozheniya

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Funktsional'nyi Analiz i ego Prilozheniya, 2006, Volume 40, Issue 3, Pages 53–65
DOI: https://doi.org/10.4213/faa743 (Mi faa743)

This article is cited in 66 scientific papers (total in 66 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

Full-text PDF (239 kB) Citations (66)

References:

PDF

HTML

DOI: https://doi.org/10.4213/faa743

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.

Received: 10.08.2005

English version:
Functional Analysis and Its Applications, 2006, Volume 40, Issue 3, Pages 207–217
DOI: https://doi.org/10.1007/s10688-006-0032-1

Bibliographic databases:

Document Type: Article

UDC: 517.958

Language: Russian

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

\Bibitem{Tsi06}

\by N.~V.~Tsilevich

\paper Quantum Inverse Scattering Method for the $q$-Boson Model and Symmetric Functions

\jour Funktsional. Anal. i Prilozhen.

\yr 2006

\vol 40

\issue 3

\pages 53--65

\mathnet{http://mi.mathnet.ru/faa743}

\crossref{https://doi.org/10.4213/faa743}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2265685}

\zmath{https://zbmath.org/?q=an:1118.81041}

\elib{https://elibrary.ru/item.asp?id=9296643}

\transl

\jour Funct. Anal. Appl.

\yr 2006

\vol 40

\issue 3

\pages 207--217

\crossref{https://doi.org/10.1007/s10688-006-0032-1}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000241583800006}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33749537065}

Linking options:

https://www.mathnet.ru/eng/faa743

https://doi.org/10.4213/faa743

https://www.mathnet.ru/eng/faa/v40/i3/p53

This publication is cited in the following 66 articles:

Paul Zinn-Justin, Encyclopedia of Mathematical Physics, 2025, 127
Xin Zhang, Zhaowen Yan, “The fermion representation of the generalized phase model”, Nuclear Physics B, 1002 (2024), 116532
Sergei Korotkikh, “Representation theoretic interpretation and interpolation properties of inhomogeneous spin q-Whittaker polynomials”, Sel. Math. New Ser., 30:3 (2024)
Rui An, Zhaowen Yan, “The generalization of strong anisotropic XXZ model and UC hierarchy”, Anal.Math.Phys., 14:2 (2024)
Alexei Borodin, Sergei Korotkikh, “Inhomogeneous spin q-Whittaker polynomials”, Annales de la Faculté des sciences de Toulouse : Mathématiques, 33:1 (2024), 1
Ben Brubaker, Valentin Buciumas, Daniel Bump, Henrik P. A. Gustafsson, “Colored vertex models and Iwahori Whittaker functions”, Sel. Math. New Ser., 30:4 (2024)
Thiago Araujo, “Q-boson model and relations with integrable hierarchies”, Nuclear Physics B, 1006 (2024), 116640
Ben Brubaker, Will Grodzicki, Andrew Schultz, “Special Functions for Hyperoctahedral Groups Using Bosonic Lattice Models”, Ann. Comb., 2024
Na Wang, “3-JACK POLYNOMIALS AND YANG–BAXTER EQUATION”, Reports on Mathematical Physics, 91:1 (2023), 79
Amol Aggarwal, Alexei Borodin, Leonid Petrov, Michael Wheeler, “Free fermion six vertex model: symmetric functions and random domino tilings”, Sel. Math. New Ser., 29:3 (2023)
Na Wang, Can Zhang, Ke Wu, “3D boson representation of affine Yangian of gl(1) and 3D cut-and-join operators”, Journal of Mathematical Physics, 64:11 (2023)
Na Wang, Ke Wu, “3D bosons, 3-Jack polynomials and affine Yangian of $ \mathfrak{gl}(1) $”, J. High Energ. Phys., 2023:3 (2023)
Jan Felipe van Diejen, “Spectrum and Orthogonality of the Bethe Ansatz for the Periodic q-Difference Toda Chain on ${\mathbb {Z}}_{m+1}$”, Ann. Henri Poincaré, 24:6 (2023), 1877
van Diejen J.F., “Harmonic Analysis of Boxed Hyperoctahedral Hall-Littlewood Polynomials”, J. Funct. Anal., 282:1 (2022), 109256
Alexei Borodin, Michael Wheeler, “Nonsymmetric Macdonald polynomials via integrable vertex models”, Trans. Amer. Math. Soc., 375:12 (2022), 8353
Borodin A., Wheeler M., “Spin Q-Whittaker Polynomials”, Adv. Math., 376 (2021), 107449
Pozsgay B., Gombor T., Hutsalyuk A., Jiang Yu., Pristyak L., Vernier E., “Integrable Spin Chain With Hilbert Space Fragmentation and Solvable Real-Time Dynamics”, Phys. Rev. E, 104:4 (2021), 044106
Corteel S., Gitlin A., Keating D., Meza J., “A Vertex Model For Llt Polynomials”, Int. Math. Res. Notices, 2021
Wang N., Shi L., “Affine Yangian and Schur Functions on Plane Partitions of 4”, J. Math. Phys., 62:6 (2021), 061701
Hutsalyuk A., Pozsgay B., “Integrability Breaking in the One-Dimensional Bose Gas: Atomic Losses and Energy Loss”, Phys. Rev. E, 103:4 (2021), 042121

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

Functional Analysis and Its Applications

Statistics & downloads:
Abstract page:	647
Full-text PDF :	262
References:	76
First page:	2

Registration to the website

Logotypes