Quantized W-algebra of sl(2,1) and quantum parafermions of U_q(sl(2))

Abstract

In this paper, we establish the connection between the quantized W-algebra of ${\frak sl}(2,1)$ and quantum parafermions of $U_q(\hat {\frak sl}(2))$ that a shifted product of the two quantum parafermions of $U_q(\hat {\frak sl}(2))$ generates the quantized W-algebra of ${\frak sl}(2,1)$.