Highest weights for truncated shifted Yangians and product monomial crystals
Representation Theory
2022-11-18 v2 Algebraic Geometry
Abstract
Truncated shifted Yangians are a family of algebras which are natural quantizations of slices in the affine Grassmannian. We study the highest weight representations of these algebras. In particular, we conjecture that the possible highest weights for these algebras are described by product monomial crystals, certain natural subcrystals of Nakajima's monomials. We prove this conjecture in type A. We also place our results in the context of symplectic duality and prove a conjecture of Hikita in this situation.
Keywords
Cite
@article{arxiv.1511.09131,
title = {Highest weights for truncated shifted Yangians and product monomial crystals},
author = {Joel Kamnitzer and Peter Tingley and Ben Webster and Alex Weekes and Oded Yacobi},
journal= {arXiv preprint arXiv:1511.09131},
year = {2022}
}
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57 pages