Braided central elements
Representation Theory
2007-05-23 v1 Quantum Algebra
Abstract
We present and study two families of polynomials with coefficients in the center of the universal enveloping algebra. These polynomials are analogues of a determinant and a characteristic polynomial of a certain non-commutative matrix, labeled by irreducible representations of gl(n,C). The matrix is an image of the universal R-matrix of a Yangian of gl(n,C) under certain representation. We compute the polynomials explicitly for gl(2,C) and establish connections between the first family of polynomials and higher Capelli identities through some sort of plethysm.
Cite
@article{arxiv.math/0510226,
title = {Braided central elements},
author = {Natasha Rozhkovskaya},
journal= {arXiv preprint arXiv:math/0510226},
year = {2007}
}
Comments
13 pages