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

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 $U_q(gl(2r+1|2s{)}^{(2)})$, $U_q(gl(2r|2s+1{)}^{(2)})$, $U_q(gl(2r|2s{)}^{(2)})$, $U_q(osp(2r|2s{)}^{(2)})$ and the untwisted quantum affine orthosymplectic superalgebras $U_q(osp(2r+1|2s{)}^{(1)})$ and $U_q(osp(2r|2s{)}^{(1)})$ (and their Yangian counterparts, $Y(osp(2r+1|2s))$ and $Y(osp(2r|2s))$) as reductions (a kind of folding) of those associated with $U_q(gl(M|N{)}^{(1)})$. 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 $U_q(gl(M|N{)}^{(1)})$.

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

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Cited by in corpus (3)

• Orthosymplectic superoscillator Lax matrices
• The ODE/IM Correspondence between $C(2{)}^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT
• Character Formulas for Kirillov-Reshetikhin Modules via Folding of Supercharacters of $\mathfrak{gl}(M|N)$