Eigenvalues of quantum Gelfand invariants
Quantum Algebra
2024-06-13 v4 Mathematical Physics
math.MP
Representation Theory
Abstract
We consider the quantum Gelfand invariants which first appeared in a landmark paper by Reshetikhin, Takhtadzhyan and Faddeev (1989). We calculate the eigenvalues of the invariants acting in irreducible highest weight representations of the quantized enveloping algebra for . The calculation is based on Liouville-type formulas relating two families of central elements in the quantum affine algebras of type .
Cite
@article{arxiv.2312.13815,
title = {Eigenvalues of quantum Gelfand invariants},
author = {Naihuan Jing and Ming Liu and Alexander Molev},
journal= {arXiv preprint arXiv:2312.13815},
year = {2024}
}
Comments
13 pages, construction of central elements and some proofs were simplified in v2, limit values as q->1 are discussed in v3, reference to earlier work on Liouville formula added in v4