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## Generalized Weyl modules, alcove paths and Macdonald polynomials

arxiv.org. math. Cornell University, 2015. No. 1512.03254.
Feigin E., Makedonskyi I.
The classical local Weyl modules for a simple Lie algebra are labeled by dominant weights. We generalize the definition to the case of arbitrary weights and study the properties of the generalized modules. We prove that the representation theory of the generalized Weyl modules can be described in terms of the alcove paths and the quantum Bruhat graph. We make use of the Orr-Shimozono formula for the nonsymmetric Macdonald polynomials in order to prove that the t=∞ specialization of the nonsymmetric Macdonald polynomials are equal to the characters of the generalized Weyl modules corresponding to the antidominant weights. We also prove a generalization of the t=0 specialization theorem by Ion to the case of the non simply-laced algebras.