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.
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}
}