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

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

1995-06-16

arxiv.org/abs/q-alg/9506016v2

J.Phys. A28 (1995) 5589-5606

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, LaTeX 2.09 (and amsfonts preferably). (Minor corrections)

Scientific paper

10.1088/0305-4470/28/19/014

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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