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BRST Cohomology in Quantum Affine Algebra $U_q(\widehat{sl_2})$

Hitoshi Konno
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Abstract

Using free field representation of quantum affine algebra $U_q(\widehat{sl_2})$, we investigate the structure of the Fock modules over $U_q(\widehat{sl_2})$. The analisys is based on a $q$-analog of the BRST formalism given by Bernard and Felder in the affine Kac-Moody algebra $\widehat {sl_2}$. We give an explicit construction of the singular vectors using the BRST charge. By the same cohomology analysis as the classical case ($q=1$), we obtain the irreducible highest weight representation space as a nontrivial cohomology group. This enables us to calculate a trace of the $q$-vertex operators over this space.

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Hitoshi Konno. 1993-10-18. BRST Cohomology in Quantum Affine Algebra $U_q(\widehat{sl_2})$. https://doi.org/10.1142/s0217732394001076

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