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Level-0 structure of level-1 $U_q(\widehat{sl}_2)$-modules and Macdonald polynomials

M. Jimbo·R. Kedem·H. Konno·T. Miwa·J. -U. H. Petersen
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Abstract

The level-$1$ integrable highest weight modules of $U_q(\widehat{sl}_2)$ admit a level-$0$ action of the same algebra. This action is defined using the affine Hecke algebra and the basis of the level-$1$ module generated by components of vertex operators. Each level-$1$ module is a direct sum of finite-dimensional irreducible level-$0$ modules, whose highest weight vector is expressed in terms of Macdonald polynomials. This decomposition leads to the fermionic character formula for the level-$1$ modules.

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BibTeXRIS

M. Jimbo, R. Kedem, H. Konno, T. Miwa, J. -U. H. Petersen. 1995-07-26. Level-0 structure of level-1 $U_q(\widehat{sl}_2)$-modules and Macdonald polynomials. https://doi.org/10.1088/0305-4470%2F28%2F19%2F014

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