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JOURNALS // Moscow Mathematical Journal // Archive

Mosc. Math. J., 2003 Volume 3, Number 4, Pages 1247–1267 (Mi mmj130)

A construction of level 1 irreducible modules for $U_q(\widehat{\mathfrak{sp}}_4)$ using level 2 intertwiners for $U_q(\widehat{\mathfrak{sl}}_2)$

B. L. Feigina, J. Hongb, T. Miwac

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Korea Institute for Advanced Study
c Kyoto University

Abstract: We bosonize certain components of level $l$ $U_q(\widehat{\mathfrak{sl}}_2)$-intertwiners of $(l+1)$-dimensions. For $l=2$, these intertwiners, after certain modification by bosonic vertex operators, are added to the algebra $U_q(\widehat{\mathfrak{sl}}_2)$ at level 2 to construct all irreducible highest weight representations of level 1 for the quantum affine algebra $U_q(\widehat{\mathfrak{sp}}_4)$.

Key words and phrases: Quantized enveloping algebra, $\widehat{\mathfrak{sp}}_4$, irreducible representation, extended vertex operator.

MSC: Primary 17B37; Secondary 17B69

Received: January 21, 2002

Language: English

DOI: 10.17323/1609-4514-2003-3-4-1247-1267



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