Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains

Zengo Tsuboi

doi:10.1016/j.nuclphysb.2024.116607

paper

Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains

arXiv:2309.16660 · doi:10.1016/j.nuclphysb.2024.116607

Abstract

Extending the method proposed in [arXiv:1109.5524], we derive QQ-relations (functional relations among Baxter Q-functions) and T-functions (eigenvalues of transfer matrices) for fusion vertex models associated with the twisted quantum affine superalgebras $U_{q} (g l (2 r + 1∣2 s)^{(2)})$ , $U_{q} (g l (2 r ∣2 s + 1)^{(2)})$ , $U_{q} (g l (2 r ∣2 s)^{(2)})$ , $U_{q} (os p (2 r ∣2 s)^{(2)})$ and the untwisted quantum affine orthosymplectic superalgebras $U_{q} (os p (2 r + 1∣2 s)^{(1)})$ and $U_{q} (os p (2 r ∣2 s)^{(1)})$ (and their Yangian counterparts, $Y (os p (2 r + 1∣2 s))$ and $Y (os p (2 r ∣2 s))$ ) as reductions (a kind of folding) of those associated with $U_{q} (g l (M ∣ N)^{(1)})$ . In particular, we reproduce previously proposed generating functions (difference operators) of the T-functions for the symmetric or anti-symmetric representations, and tableau sum expressions for more general representations for orthosymplectic superalgebras [arXiv:0911.5393,arXiv:0911.5390], and obtain Wronskian-type expressions (analogues of Weyl-type character formulas) for them. T-functions for spinorial representations are related to reductions of those for asymptotic limits of typical representations of $U_{q} (g l (M ∣ N)^{(1)})$ .

101 pages, v2: an appendix added; v3: small improvements; v4 misprints corrected