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Flag varieties for the Yangian Y(gl_n)

Research paper by Aaron Lauve

Indexed on: 03 Jan '06Published on: 03 Jan '06Published in: Mathematics - Quantum Algebra



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.