Geometric and combinatorial realizations of crystal graphs
Representation Theory
2012-02-28 v4 Algebraic Geometry
Quantum Algebra
Abstract
For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver varieties and the combinatorial realizations in terms of Young tableaux and Young walls. For affine type A, we extend the Young wall construction to arbitrary level, describing a combinatorial realization of the crystals in terms of new objects which we call Young pyramids.
Cite
@article{arxiv.math/0310314,
title = {Geometric and combinatorial realizations of crystal graphs},
author = {Alistair Savage},
journal= {arXiv preprint arXiv:math/0310314},
year = {2012}
}
Comments
34 pages, 17 figures; v2: minor typos corrected; v3: corrections to section 8; v4: minor typos corrected