This article is cited in 16 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.

MSC: 81R10, 17B37, 81R50

Received: January 8, 2012; in final form May 10, 2012; Published online May 15, 2012

Language: English

DOI: 10.3842/SIGMA.2012.028

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ArXiv: 1201.1614