Jacobi-Trudi identity and Drinfeld functor for super Yangian

Abstract

We show that the quantum Berezinian which gives a generating function of the integrals of motions of XXX spin chains associated to super Yangian $\mathrm{Y}({\mathfrak{gl}}_{m|n})$ can be written as a ratio of two difference operators of orders $m$ and $n$ whose coefficients are ratios of transfer matrices corresponding to explicit skew Young diagrams. In the process, we develop several missing parts of the representation theory of $\mathrm{Y}({\mathfrak{gl}}_{m|n})$ such as $q$-character theory, Jacobi-Trudi identity, Drinfeld functor, extended T-systems, Harish-Chandra map.

arXiv commentLaTeX, 35 pages, several figures; V2: added more details

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Cited by in corpus (14)

• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• A note on odd reflections of super Yangian and Bethe ansatz
• Representations of the super Yangians of types $A$ and $C$
• Bethe ansatz equations for orthosymplectic Lie superalgebras and self-dual superspaces
• Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra
• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
• Double Yangian and reflection algebras of the Lie superalgebra ${\mathfrak{gl}}_{m|n}$
• Completeness of Bethe ansatz for Gaudin models associated with gl(1|1)
• On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
• Schur-Weyl duality for quantum toroidal superalgebras
• A note on the quantum Berezinian for the double Yangian of the Lie superalgebra ${\mathfrak{gl}}_{m|n}$
• Twisted super Yangians of type AIII and their representations
• Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system
• Quantum Berezinian for quantum affine superalgebra $U_q({\widehat{gl}}_{M|N})$