Vol. 286, No. 2, 2017

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ISSN: 0030-8730
The symplectic plactic monoid, crystals, and MV cycles

Jacinta Torres

Vol. 286 (2017), No. 2, 439–497

We study cells in generalized Bott–Samelson varieties for type Cn. 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.

Littelmann path model, combinatorics of MV cycles, buildings, affine Grassmannian
Mathematical Subject Classification 2010
Primary: 05E10, 17B10, 22E47, 22E57
Secondary: 14R99
Received: 17 September 2015
Revised: 28 April 2016
Accepted: 4 May 2016
Published: 15 January 2017
Jacinta Torres
Max Planck Institute for Mathematics
Vivatsgasse 7
D-53111 Bonn