Titlebook: Quantum Groups in Three-Dimensional Integrability; Atsuo Kuniba Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive

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,Boundary Vector Reductions of , reflection equation . and perform the boundary vector reduction. The . part gives rise to the quantum . matrices for the spin representations of ., which have been detailed in Chap. .. The . part generates the companion . matrices that satisfy the reflection equation. They are expressed by a matrix

biopsy

Reductions of Quantized , Reflection Equation,or relative rapidity, of the world lines of particles that undergo factorized scattering in integrable .D quantum field theories in the bulk and at the boundary. There is an analogous equation associated with ., which we call the . . in this book. It describes the three-body scattering related to th

致词

Density

3D , From Quantized Coordinate Ring of Type A,rring a more universal formulation to Sect. .. It turns out that an intertwiner of certain . modules leads to a 3D ., a solution of the tetrahedron equation. It has set-theoretical and birational counterparts which satisfy the tetrahedron equation in the respective setting. The birational case admits bilinearization in terms of tau functions.

Haphazard

Connection to PBW Bases of Nilpotent Subalgebra of ,the transition matrix of the corresponding PBW bases of .. It leads to an alternative proof of the tetrahedron and 3D reflection equations within .. The boundary vectors in Sects. ., . and . give rise to invariants of an anti-algebra involution in . in an infinite product form.

绝缘

,Boundary Vector Reductions of ,., . and .. These algebras have Dynkin diagrams with double outward arrows or double branches. It turns out that the two kinds of the boundary vectors correspond to the two choices of the end shape of the relevant Dynkin diagrams. For simplicity, we treat the reduction with respect to the .-oscillator Fock space only.

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Book 2022eir discovery in the mid-1980s. Roughly speaking, there are two prototype examples of quantum groups, denoted by .U.q. and .A.q.. The former is a deformation of the universal enveloping algebra of a Kac–Moody Lie algebra, whereas the latter is a deformation of the coordinate ring of a Lie group. Alt

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choleretic

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Intertwiners for Quantized Coordinate Ring ,. As suggested by the relevant Dynkin diagrams, it consists of a mixture of . and . structures, and is attributed to a composition of the 3D reflection equations . of type B and . of type C twelve times for each.