Flag varieties for the Yangian Y(gl_n)
Quantum Algebra
2007-05-23 v1
Abstract
We show that the Yangian Yn over gl_n possesses some features of the ring of regular functions on GL_n. In particular, we use the theory of quasideterminants to construct noncommutative flags associated to Yn. In so doing, a class of comodule algebras Fl(\gamma) for Yn (viewed as C[GL_n]) is revealed. As in the classic case, these flag algebras are related to the irreducible representations of Yn (viewed as U(gl_n)). In the course of defining the rings Fl(\gamma), connections to the new parabolic presentations of Yn given by Brundan and Kleshchev (2005) are uncovered.
Cite
@article{arxiv.math/0601056,
title = {Flag varieties for the Yangian Y(gl_n)},
author = {Aaron Lauve},
journal= {arXiv preprint arXiv:math/0601056},
year = {2007}
}
Comments
30 pages