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- W4317433080 abstract "We obtain BGG-type formulas for transfer matrices of irreducible finite-dimensional representations of the classical Lie algebras $${mathfrak {g}}$$ , whose highest weight is a multiple of a fundamental one and which can be lifted to the representations over the Yangian $$Y({mathfrak {g}})$$ . These transfer matrices are expressed in terms of transfer matrices of certain infinite-dimensional highest weight representations (such as parabolic Verma modules and their generalizations) in the auxiliary space. We further factorise the corresponding infinite-dimensional transfer matrices into the products of two Baxter Q-operators, arising from our previous study Frassek et al. (Adv. Math. 401:108283, 2022), Frassek and Tsymbaliuk (Commun. Math. Phys. 392:545–619, 2022) of the degenerate Lax matrices. Our approach is crucially based on the new BGG-type resolutions of the finite-dimensional $${mathfrak {g}}$$ -modules, which naturally arise geometrically as the restricted duals of the Cousin complexes of relative local cohomology groups of ample line bundles on the partial flag variety G/P stratified by $$B_{-}$$ -orbits." @default.
- W4317433080 created "2023-01-19" @default.
- W4317433080 creator A5023669710 @default.
- W4317433080 creator A5043554819 @default.
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- W4317433080 date "2023-02-10" @default.
- W4317433080 modified "2023-09-26" @default.
- W4317433080 title "Transfer Matrices of Rational Spin Chains via Novel BGG-Type Resolutions" @default.
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- W4317433080 doi "https://doi.org/10.1007/s00220-022-04620-6" @default.
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