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SIGMA, 2012, Volume 8, 028, 34 pages (Mi sigma705)  

This article is cited in 9 scientific papers (total in 9 papers)

Polynomial relations for $q$-characters via the ODE/IM correspondence

Juanjuan Sun

Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo 153-8914, Japan

Abstract: Let $U_q(\mathfrak{b})$ be the Borel subalgebra of a quantum affine algebra of type $X^{(1)}_n$ ($X=A,B,C,D$). Guided by the ODE/IM correspondence in quantum integrable models, we propose conjectural polynomial relations among the $q$-characters of certain representations of $U_q(\mathfrak{b})$.

Keywords: Borel subalgebra, $q$-character, Baxter's $Q$-operator, ODE/IM correspondence.

DOI: https://doi.org/10.3842/SIGMA.2012.028

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Bibliographic databases:

ArXiv: 1201.1614
MSC: 81R10, 17B37, 81R50
Received: January 8, 2012; in final form May 10, 2012; Published online May 15, 2012
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Citation: Juanjuan Sun, “Polynomial relations for $q$-characters via the ODE/IM correspondence”, SIGMA, 8 (2012), 028, 34 pp.

Citation in format AMSBIB
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\by Juanjuan Sun
\paper Polynomial relations for $q$-characters via the ODE/IM correspondence
\jour SIGMA
\yr 2012
\vol 8
\papernumber 028
\totalpages 34
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. Ito, Ch. Locke, “ODE/IM correspondence and modified affine Toda field equations”, Nucl. Phys. B, 885 (2014), 600–619  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. E. Frenkel, D. Hernandez, “Baxter's relations and spectra of quantum integrable models”, Duke Math. J., 164:12 (2015), 2407–2460  crossref  mathscinet  zmath  isi  elib  scopus
    3. K. Ito, Ch. Locke, “ODE/IM correspondence and Bethe ansatz for affine Toda field equations”, Nucl. Phys. B, 896 (2015), 763–778  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. D. Masoero, A. Raimondo, D. Valeri, “Bethe ansatz and the spectral theory of affine Lie algebra-valued connections I: The simply-laced case”, Commun. Math. Phys., 344:3 (2016), 719–750  crossref  mathscinet  zmath  isi  elib  scopus
    5. K. Ito, H. Shu, “ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation”, Nucl. Phys. B, 916 (2017), 414–429  crossref  mathscinet  zmath  isi  scopus
    6. D. Masoero, A. Raimondo, D. Valeri, “Bethe ansatz and the spectral theory of affine Lie algebra-valued connections II: The non simply-laced case”, Commun. Math. Phys., 349:3 (2017), 1063–1105  crossref  mathscinet  zmath  isi  scopus
    7. K. Ito, H. Shu, “ODE/IM correspondence and the Argyres–Douglas theory”, J. High Energy Phys., 2017, no. 8, 071  crossref  mathscinet  isi  scopus
    8. K. Ito, H. Shu, “Massive ODE/IM correspondence and nonlinear integral equations for $A_r^{(1)}$ -type modified affine Toda field equations”, J. Phys. A-Math. Theor., 51:38 (2018), 385401  crossref  isi  scopus
    9. E. Frenkel, D. Hernandez, “Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers”, Commun. Math. Phys., 362:2 (2018), 361–414  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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