Weyl, Fusion and Demazure modules for the current algebra of sl_{r+1}

Details Weyl, Fusion and Demazure modules for the current algebra of sl_{r+1} Weyl, Fusion and Demazure modules for the current algebra of sl_{r+1}

2005-02-08

arxiv.org/abs/math/0502165v2

Advances in Mathematics, 207 (2006), 928-960

Mathematics

Quantum Algebra

26 pages, LaTeX; final version, minor changes

Scientific paper

We construct a Poincare-Birkhoff-Witt type basis for the Weyl modules of the current algebra of $sl_{r+1}$. As a corollary we prove a conjecture made by Chari and Pressley on the dimension of the Weyl modules in this case. Further, we relate the Weyl modules to the fusion modules of the current algebra defined by Feigin and Loktev, and to the Demazure modules in level one representations of the corresponding affine algebra. In particular, this allows us to establish substantial cases of the conjectures of Feigin and Loktev on the structure and graded character of the fusion modules.

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