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

Hitoshi Konno

doi:10.1142/S0217732394001076

paper

BRST Cohomology in Quantum Affine Algebra $U_{q} (s l_{2})$

arXiv:hep-th/9310108 · doi:10.1142/S0217732394001076

Abstract

Using free field representation of quantum affine algebra $U_{q} (s l_{2})$ , we investigate the structure of the Fock modules over $U_{q} (s l_{2})$ . The analisys is based on a $q$ -analog of the BRST formalism given by Bernard and Felder in the affine Kac-Moody algebra $s l_{2}$ . 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.

14 pages, RIMS-927

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BRST Cohomology in Quantum Affine Algebra Uq​(sl2​​)

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BRST Cohomology in Quantum Affine Algebra $U_{q} (s l_{2})$