Odd-reflection isomorphism conjecture for the super Yangian of D(2,1;λ)D(2,1;\lambda)

Let D(2,1;λ)D(2,1;\lambda) be the exceptional Lie superalgebra with Dynkin diagrams G(Dλ)G(D_{\lambda}) and G(Dλ)G(D_{\lambda}^{\circ}) related by the odd reflection sα2s_{\alpha_2}, and let Y(D^λ)Y_{\hbar}(\widehat{D}_{\lambda}) and Y(D^λ)Y_{\hbar}(\widehat{D}_{\lambda}^{\circ}) denote the corresponding super Yangians. Odd-reflection isomorphism conjecture. The super Yangians

Y(D^λ)andY(D^λ)Y_{\hbar}(\widehat{D}_{\lambda})\quad\text{and}\quad Y_{\hbar}(\widehat{D}_{\lambda}^{\circ})

are isomorphic. Odd reflections can change Dynkin diagrams of Lie superalgebras, and the corresponding quantum affine superalgebras are known to be isomorphic. The conjecture proposes the analogous isomorphism for the associated super Yangians.

Sources & referencesView supporting material

Primary source

Hongda Lin and Honglian Zhang, “Drinfeld super Yangian of the exceptional Lie superalgebra D(2,1;λ)”, arXiv:2504.21255 (2025).

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