representation theory

On weight modules over truncated shifted iYangians

arXiv:2607.27596

summary

The paper studies truncated shifted iYangians, introducing orientifold KLRW algebras and establishing diagrammatic and polynomial representations, and proves an equivalence between integral weight modules of these iYangians and nilpotent modules over interval oKLRW algebras.

Abstract

Truncated shifted iYangians are a family of algebras expected to quantize certain components of affine Grassmannian islices. We introduce orientifold KLRW (oKLRW) algebras associated with quivers with involution and establish their faithful polynomial representations and diagrammatic bases. We also define KLR iYangians using double reflective KLR diagrams and construct diagrammatic realizations of the iGKLO homomorphisms. For integral parameters, we introduce interval oKLRW algebras and prove an equivalence between integral weight modules over truncated shifted iYangians and nilpotent modules over the corresponding interval oKLRW algebras.

51 pages, comments welcome!

Topics & keywords

#yangians#kLR algebras#quiver involution#affine Grassmannian#weight modulestruncated shifted iYangiansorientifold KLRW algebraspolynomial representationsdiagrammatic basesinterval oKLRW algebrasnilpotent modules