QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains

Abstract

We propose the full system of Baxter Q-functions (QQ-system) for the integrable spin chains with the symmetry of the $D_r$ Lie algebra. We use this QQ-system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and antisymmetric (fundamental) representations through $r+1$ basic Q-functions. Our functional relations are consistent with the Q-operators proposed recently by one of the authors and verified explicitly on the level of operators at small finite length.

42 pages, 9 Figures; v2: typos fixed, references added; v3: references added, section 9 improved