#### Vol. 286, No. 2, 2017

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The symplectic plactic monoid, crystals, and MV cycles

### Jacinta Torres

Vol. 286 (2017), No. 2, 439–497
##### Abstract

We study cells in generalized Bott–Samelson varieties for type ${C}_{n}$. These cells are parametrized by certain galleries in the affine building. We define a set of readable galleries — we show that the closure in the affine Grassmannian of the image of the cell associated to a gallery in this set is an MV cycle. This then defines a map from the set of readable galleries to the set of MV cycles, which we show to be a morphism of crystals. We further compute the fibers of this map in terms of the Littelmann path model.

##### Keywords
Littelmann path model, combinatorics of MV cycles, buildings, affine Grassmannian
##### Mathematical Subject Classification 2010
Primary: 05E10, 17B10, 22E47, 22E57
Secondary: 14R99