Affine PBW bases and affine MV polytopes
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We show how affine PBW bases can be used to construct affine MV polytopes, and that the resulting objects agree with the affine MV polytopes recently constructed using either preprojective algebras or KLR algebras. To do this we first generalize work of Beck–Chari–Pressley and Beck–Nakajima to define affine PBW bases for arbitrary convex orders on positive roots. Our results describe how affine PBW bases for different convex orders are related, answering a question posed by Beck and Nakajima.
KeywordsAffine MV polytope Quantum affine algebra PBW basis Crystal
Mathematics Subject ClassificationPrimary 17B37 Secondary 17B67 81R10
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We thank Joel Kamnitzer and Peter McNamara for many useful discussions. D.M. was supported by a PIMS Postdoctoral Fellowship. P.T. was partially supported by NSF Grant DMS-1265555.