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TMF, 2008, Volume 154, Number 2, Pages 240–248 (Mi tmf6165)  

Toward a vertex operator construction of quantum affine algebras

S. E. Klevtsovab

a M. V. Lomonosov Moscow State University
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: We describe a construction of the quantum-deformed affine algebras using vertex operators in the free field theory. We prove the Serre relations for the Borel subalgebras of quantum affine algebras; in particular, we consider the $\widehat{sl}_2$ case in detail. We also construct the generators corresponding to the positive roots of $\widehat{sl}_2$.

Keywords: quantum group, quantum affine algebra, free field theory, minimal model, Serre relations

DOI: https://doi.org/10.4213/tmf6165

Full text: PDF file (406 kB)
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English version:
Theoretical and Mathematical Physics, 2008, 154:2, 201–208

Bibliographic databases:

Received: 16.01.2006
Revised: 08.08.2007

Citation: S. E. Klevtsov, “Toward a vertex operator construction of quantum affine algebras”, TMF, 154:2 (2008), 240–248; Theoret. and Math. Phys., 154:2 (2008), 201–208

Citation in format AMSBIB
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\paper Toward a vertex operator construction of quantum affine algebras
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