Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system

Zengo Tsuboi

doi:10.1016/j.nuclphysb.2021.115563

paper

Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system

arXiv:2106.08931 · doi:10.1016/j.nuclphysb.2021.115563

Abstract

It is known that there is a correspondence between representations of superalgebras and ordinary (non-graded) algebras. Keeping in mind this type of correspondence between the twisted quantum affine superalgebra $U_{q} (g l (2 r ∣1)^{(2)})$ and the non-twisted quantum affine algebra $U_{q} (so (2 r + 1)^{(1)})$ , we proposed, in the previous paper [arXiv:1109.5524], a Wronskian solution of the T-system for $U_{q} (so (2 r + 1)^{(1)})$ as a reduction (folding) of the Wronskian solution for the non-twisted quantum affine superalgebra $U_{q} (g l (2 r ∣1)^{(1)})$ . In this paper, we elaborate on this solution, and give a proof missing in [arXiv:1109.5524]. In particular, we explain its connection to the Cherednik-Bazhanov-Reshetikhin (quantum Jacobi-Trudi) type determinant solution known in [arXiv:hep-th/9506167]. We also propose Wronskian-type expressions of T-functions (eigenvalues of transfer matrices) labeled by non-rectangular Young diagrams, which are quantum affine algebra analogues of the Weyl character formula for $so (2 r + 1)$ . We show that T-functions for spinorial representations of $U_{q} (so (2 r + 1)^{(1)})$ are related to reductions of T-functions for asymptotic typical representations of $U_{q} (g l (2 r ∣1)^{(1)})$ .

arXiv comment28 pages, v2: minor corrections; v3: misspellings corrected; v4: note added; v5: conditions for (A2) corrected, some other algebras cases are published in Nucl. Phys. B 1005 (2024) 116607 [arXiv:2309.16660]

Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system

Abstract

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