Bethe subalgebras in twisted Yangians

1995/07/31 by Maxim Nazarov, Grigori Olshanski · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #math.QA #q-alg #semigroups and automata theory

paper · pdf · doi:10.1007/bf02099459

published as Comm. Math. Phys. 178 (1996), 483-506 · 26 pages, amstex, misprints corrected

arxiv created 1996/01/22 · openalex publication_date 1996/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study analogues of the Yangian of the Lie algebra gl_N for the other classical Lie algebras so_N and sp_N. We call them twisted Yangians. They are coideal subalgebras in the Yangian Y(gl_N) of gl_N and admit homomorphisms onto the universal enveloping algebras U(so_N) and U(sp_N) respectively. In every twisted Yangian we construct a family of maximal commutative subalgebras parametrized by the regular semisimple elements of the corresponding classical Lie algebra. The images in U(so_N) and U(sp_N) of these subalgebras are also maximal commutative.

Citations

• Quantum symmetric spaces and related q-orthogonal polynomials
• Boundary conditions for integrable quantum systems
• Lie Group Representations on Polynomial Rings

Cited by

• Lax matrices from antidominantly shifted Yangians and quantum affine algebras: A-type