The Elliptic Algebra Uq,p(s-fraktur sign lN) and the Drinfeld Realization of the Elliptic Quantum Group B q,λ(s-fraktur sign lN)

Takeo Kojima, Hitoshi Konno

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

By using the elliptic analogue of the Drinfeld currents in the elliptic algebra Uq,p(s-fraktur sign lN), we construct a L-operator, which satisfies the RLL-relations characterizing the face type elliptic quantum group Bq,?(s-fraktur sign lN). For this purpose, we introduce a set of new currents Kj(v) (1 = j > N) in Uq,p(s-fraktur sign lN). As in the N = 2 case, we find a structure of Uq,p(s-fraktur sign lN) as a certain tensor product of Bq,?(s-fraktur sign lN) and a Heisenberg algebra. In the level-one representation, we give a free field realization of the currents in Uq,p(s-fraktur sign lN). Using the coalgebra structure of Bq,?(s-fraktur sign l N) and the above tensor structure, we derive a free field realization of the Uq,p(s-fraktur sign lN)-analogue of Bq,?(s-fraktur sign lN)-intertwining operators. The resultant operators coincide with those of the vertex operators in the AN-1(1)-type face model.

Original languageEnglish
Pages (from-to)405-447
Number of pages43
JournalCommunications in Mathematical Physics
Volume239
Issue number3
DOIs
Publication statusPublished - Aug 2003

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