Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 028, 34 pages      arXiv:1201.1614      https://doi.org/10.3842/SIGMA.2012.028

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

Received January 08, 2012, in final form May 10, 2012; Published online May 15, 2012

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 $U_q(\mathfrak{b})$.

Key words: Borel subalgebra; $q$-character; Baxter's $Q$-operator; ODE/IM correspondence.

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