Tetrahedron equation and quantum R matrices for infinite dimensional modules of U_q(A^{(1)}_1) and U_q(A^{(2)}_2)

Abstract

From the q-oscillator solution to the tetrahedron equation associated with a quantized coordinate ring, we construct solutions to the Yang-Baxter equation by applying a reduction procedure formulated earlier by S. Sergeev and the first author. The results are identified with the quantum R matrices for the infinite dimensional modules of U_q(A^{(1)}_1) and U_q(A^{(2)}_2) corresponding to an affinization of Verma modules of their subalgebras isomorphic to U_q(sl_2) and U_{q^4}(sl_2).

11 pages. Section 5 added

References in corpus (3)

• Quantum geometry of 3-dimensional lattices
• A Common Structure in PBW Bases of the Nilpotent Subalgebra of $U_q(\mathfrak{g})$ and Quantized Algebra of Functions
• Tetrahedron equations and nilpotent subalgebras of U_q(sl_n)

Cited by in corpus (3)

• Tetrahedron equation and quantum R matrices for $q$-oscillator representations of $U_q(A_{2n}^{(2)}),U_q(C_n^{(1)})$ and $U_q(D_{n+1}^{(2)})$
• Affinization of $q$-oscillator representations of $U_q({\mathfrak{gl}}_n)$
• Tetrahedron equation and quantum $R$ matrices for $q$-oscillator representations