Flag varieties for the Yangian Y(gln)
Abstract
We show that the Yangian Yn over gln possesses some features of the ring of regular functions on GLn. In particular, we use the theory of quasideterminants to construct noncommutative flags associated to Yn. In so doing, a class of comodule algebras Fl(γ) for Yn (viewed as C[GLn]) is revealed. As in the classic case, these flag algebras are related to the irreducible representations of Yn (viewed as U(gln)). In the course of defining the rings Fl(γ), connections to the new parabolic presentations of Yn given by Brundan and Kleshchev (2005) are uncovered.
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