Vertex operators and principal subspaces of level one for Uq((sl)over-cap2)

JOURNAL OF ALGEBRA

卷:455

Article

Kozic, Slaven^1,2 

[1] Univ Sydney, Sch Math & Stat F07, Sydney, NSW 2006, Australia

[2] Univ Zagreb, Dept Math, Bijenicka Cesta 30, Zagreb 10000, Croatia

关键词: Affine Lie algebra;    Quantum affine algebra;    Quantum vertex algebra;    Principal subspace;    Quasi-particle;    Combinatorial basis;   

DOI  :  10.1016/j.jalgebra.2016.01.041

来源: Elsevier

【 摘 要 】

We consider two different methods of associating vertex algebraic structures with the level 1 principal subspaces for U-q((sl) over cap (2)). In the first approach, we introduce certain commutative operators and study the corresponding vertex algebra and its module. We find combinatorial bases for these objects and show that they coincide with the principal subspace bases found by B.L. Feigin and A.V. Stoyanovsky. In the second approach, we introduce the, so-called nonlocal q-vertex algebras, investigate their properties and construct The nonlocal q-vertex algebra and its module, generated by Frenkel-Jing operator and Koyama's operator respectively. By finding the combinatorial bases of their suitably defined subspaces, we establish a connection with the sum sides of the Rogers-Ramanujan identities. Finally, we discuss further applications to quantum quasi-particle relations. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free