Principal subspaces for the quantum affine vertex algebra in type $A_1^{(1)}$
Abstract
By using the ideas of Feigin and Stoyanovsky and Calinescu, Lepowsky and Milas we introduce and study the principal subspaces associated with the EtingofKazhdan quantum affine vertex algebra of integer level $k\geqslant 1$ and type $A_1^{(1)}$. We show that the principal subspaces possess the quantum vertex algebra structure, which turns to the usual vertex algebra structure of the principal subspaces of generalized Verma and standard modules at the classical limit. Moreover, we find their topological quasiparticle bases which correspond to the sum sides of certain RogersRamanujantype identities.
 Publication:

arXiv eprints
 Pub Date:
 November 2020
 arXiv:
 arXiv:2011.13072
 Bibcode:
 2020arXiv201113072B
 Keywords:

 Mathematics  Quantum Algebra;
 17B37 (Primary);
 17B69 (Secondary)
 EPrint:
 14 pages