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Title:
Fused geometry of Bethe Algebra
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Abstract:
Maximal commutative algebra of conserved charges (Bethe Algebra) admits the action of a group G related by Langlands duality to the symmetry group of the underlying integrable model. Typical approaches using nested Bethe equations, QQ-systems, and conventional computations of q-characters disguise this feature, but it is possible to extend the collection of Baxter Q-functions and offer an alternative description where the covariance under G-action is manifest.This covariant approach allows us to describe Bethe Algebra in a purely geometric way using the concept of the fused flag, to offer compact expressions for transfer matrices (q characters) in any KR representations, and to explicitly compute the spectrum of integrable models in a more efficient way than is done by nested Bethe equations. Moreover, this perspective allows us to design a new method of monodromy bootstrap to build quantum spectral curves of the AdS/CFT type systematically.
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