Tetrahedron Equation and Quantum R Matrices for q-Oscillator Representations Mixing Particles and Holes

被引：4
|
作者：
Kuniba, Atsuo [1 ]
机构：
[1] Univ Tokyo, Inst Phys, Grad Sch Arts & Sci, Tokyo 1538902, Japan
来源：
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2018年 / 14卷
关键词：
tetrahedron equation; Yang-Baxter equation; quantum groups; q-oscillator representations;
D O I：
10.3842/SIGMA.2018.067
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We construct 2(n) + 1 solutions to the Yang-Baxter equation associated with the quantum affine algebras U-q (A(n-1)((1))), U-q(A(2n)((2))), U-q(C-n((1))) and U-q(D-n+1((2))). They act on the Fock spaces of arbitrary mixture of particles and holes in general. Our method is based on new reductions of the tetrahedron equation and an embedding of the quantum affine algebras into n copies of the q-oscillator algebra which admits an automorphism interchanging particles and holes.
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页数：23
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