Chevalley restriction theorem for vector-valued functions on quantum groups
Quantum Algebra
2012-02-28 v2 Representation Theory
Abstract
We generalize Chevalley's theorem about restriction of \mathfrak{g}-invariant polynomial functions \mathfrak{g}->C to W-invariant functions on the Cartan \mathfrak{h}->C. We consider the case when \mathfrak{g} is replaced by a quantum group and the target space of the polynomial maps is replaced by a finite dimensional representation V of this quantum group. We prove that the restriction map Res:(O_q(G)\otimes V)^{U_q(\mathfrak{g})}-> O(H)\otimes V is injective and describe the image.
Keywords
Cite
@article{arxiv.1004.0371,
title = {Chevalley restriction theorem for vector-valued functions on quantum groups},
author = {Martina Balagovic},
journal= {arXiv preprint arXiv:1004.0371},
year = {2012}
}