Speaker: Huafeng Zhang (Universite de Lille)
Title: Shifted Yangians and polynomial R-matrices
Speaker's URL: https://sites.google.com/site/hzhanglille1/
Abstract: Associated to a finite-dimensional complex simple Lie algebra is a family of algebras, the shifted Yangians. In this talk we are interested in a category O of modules over these shifted Yangians. We establish cyclicity and cocyclicity properties for the tensor product of a "signed" module (which we will explain in the talk) with an arbitrary irreducible module, for all choices of spectral parameters. These properties enable us to construct the R-matrices for these tensor products and imply furthermore that these R-matrices are polynomial functions of the spectral parameter. As applications, we prove that in category O: any irreducible module factorizes through a truncated shifted Yangian; the class of modules of finite representation length is stable under tensor product.
Based on joint work with David Hernandez.
URL associated with Seminar
https://research.math.osu.edu/reps/
