English

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