Combinatorics and Geometry of Higher Level Weyl Modules

Details Combinatorics and Geometry of Higher Level Weyl Modules Combinatorics and Geometry of Higher Level Weyl Modules

2005-03-16

arxiv.org/abs/math/0503315v3

AMS Transl., Ser. 2, 221 (2007)

Mathematics

Quantum Algebra

15 pages, LaTeX

Scientific paper

A higher level analog of Weyl modules over multi-variable currents is proposed. It is shown that the sum of their dual spaces form a commutative algebra. The structure of these modules and the geometry of the projective spectrum of this algebra is studied for the currents of dimension one and two. Along the way we prove some particular cases of the conjectures in [FL1] and propose a generalization of the notion of parking function representations.

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