New boson realizations of quantum groups \(U_q (A_n)\). (English) Zbl 0963.81034

Burdík, Č.; Navrátil, O.

Slovák, Jan (ed.) et al., The proceedings of the 19th Winter School “Geometry and physics”, Srní, Czech Republic, January 9-15, 1999. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 63, 75-84 (2000).

Summary: We describe a construction of boson realizations of quantum groups. The realizations are expressed by means of \(r(n-r+1)\) \(q\)-deformed bosons pairs and generators of certain subalgebras of \(U_q(A_n)\).
For the entire collection see [Zbl 0940.00040].

MSC:

81R50	Quantum groups and related algebraic methods applied to problems in quantum theory
17B37	Quantum groups (quantized enveloping algebras) and related deformations

Keywords:

Yang-Baxter equations; \(q\)-deformed bosons pairs; boson realizations