Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 103, 19 pages      arXiv:1707.09638      https://doi.org/10.3842/SIGMA.2018.103

Virtual Crystals and Nakajima Monomials

Ben Salisbury a and Travis Scrimshaw b
a) Department of Mathematics, Central Michigan University, Mount Pleasant, MI 48859, USA
b) School of Mathematics and Physics, The University of Queensland, St. Lucia, QLD 4072, Australia

Received March 28, 2018, in final form September 20, 2018; Published online September 26, 2018

Abstract
An explicit description of the virtualization map for the (modified) Nakajima monomial model for crystals is given. We give an explicit description of the Lusztig data for modified Nakajima monomials in type $A_n$.

Key words: crystal; Nakajima monomial; virtualization; PBW basis; Kostant partition.

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