The symplectic plactic monoid, crystals, and MV cycles

Jacinta Torres

Vol. 286 (2017), No. 2, 439–497

DOI: 10.2140/pjm.2017.286.439

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

Milestones

Received: 17 September 2015

Revised: 28 April 2016

Accepted: 4 May 2016

Published: 15 January 2017