The Affine Closure of T^*(SL_n/U)
Representation Theory
2025-11-06 v2
Abstract
We show that the affine closure of T^*(SL_n/U) has symplectic singularities, in the sense of Beauville. In the special case n=3, we show that the affine closure of T^*(SL_3/U) is isomorphic to the closure of the minimal nilpotent adjoint orbit in so(8,C). Moreover, the quasi-classical Gelfand-Graev action of the Weyl group W on the affine closure of T^*(SL_3/U) can be identified with the restriction to the closure of the minimal nilpotent adjoint orbit of the triality action on so(8,C).
Keywords
Cite
@article{arxiv.2112.08649,
title = {The Affine Closure of T^*(SL_n/U)},
author = {Boming Jia},
journal= {arXiv preprint arXiv:2112.08649},
year = {2025}
}
Comments
19 pages