The symplectic plactic monoid, crystals, and MV cycles
Representation Theory
2017-01-25 v2 Combinatorics
Abstract
We study cells in generalised Bott-Samelson varieties for type C. These cells are parametrised by certain galleries in the affine building. We define a set of readable galleries - we show that the closure in the affine Grassmannian associated to a gallery in this set is an MV cycle. This then defines a map from the set of readable galeries to the set of MV cycles, which we show to be a morphism of crystals. We further compute the fibres of this map in terms of the Littelmann path model.
Cite
@article{arxiv.1407.5015,
title = {The symplectic plactic monoid, crystals, and MV cycles},
author = {Jacinta Torres},
journal= {arXiv preprint arXiv:1407.5015},
year = {2017}
}
Comments
41 pages, substantially revised