English

Contravariant form for reduction algebras and Pieri rule

Representation Theory 2018-04-18 v1 Mathematical Physics math.MP Rings and Algebras

Abstract

We study properties and constructions of contravariant forms on reduction algebras. As an application we compute norms of highest weight vectors in the tensor product of an irreducible finite dimensional representation of the Lie algebra gl(n) with a symmetric or wedge tensor power of its fundamental representation. Their zeroes describe Pieri rules.

Keywords

Cite

@article{arxiv.1707.07136,
  title  = {Contravariant form for reduction algebras and Pieri rule},
  author = {S. Khoroshkin and O. Ogievetsky},
  journal= {arXiv preprint arXiv:1707.07136},
  year   = {2018}
}