Tetrahedron equations and nilpotent subalgebras of U_q(sl_n)

Abstract

A relation between q-oscillator R-matrix of the tetrahedron equation and decompositions of Poinkare-Birkhoff-Witt type bases for nilpotent subalgebras of U_q(sl_n) is observed.

arXiv comment4 pages

References in corpus (1)

• Zamolodchikov's Tetrahedron Equation and Hidden Structure of Quantum Groups

Cited by in corpus (6)

• Tetrahedron equation and quantum R matrices for $q$-oscillator representations of $U_q(A_{2n}^{(2)}),U_q(C_n^{(1)})$ and $U_q(D_{n+1}^{(2)})$
• A Common Structure in PBW Bases of the Nilpotent Subalgebra of $U_q(\mathfrak{g})$ and Quantized Algebra of Functions
• Integrable 3D lattice model in M-theory
• Tetrahedron equation and quantum R matrices for infinite dimensional modules of U_q(A^{(1)}_1) and U_q(A^{(2)}_2)
• Tetrahedron Equation and Quantum $R$ Matrices for modular double of $U_q(D_{n+1}^{(2)}),U_q(A_{2n}^{(2)})$ and $U_q(C_n^{(1)})$
• Tetrahedron and 3D reflection equation from PBW bases of the nilpotent subalgebra of quantum superalgebras