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arXiv · 1910.07411

Nakajima quiver varieties, affine crystals and combinatorics of Auslander-Reiten quivers

Deniz Kus·Bea Schumann
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Abstract

We obtain an explicit crystal isomorphism between two realizations of crystal bases of finite dimensional irreducible representations of simple Lie algebras of type A and D. The first realization we consider is a geometric construction in terms of irreducible components of certain Nakajima quiver varieties established by Saito and the second is a realization in terms of isomorphism classes of quiver representations obtained by Reineke. We give a homological description of the irreducible components of Lusztig's quiver varieties which correspond to the crystal of a finite dimensional representation and describe the promotion operator in type A to obtain a geometric realization of Kirillov-Reshetikhin crystals.

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BibTeXRIS

Deniz Kus, Bea Schumann. 2019-10-16. Nakajima quiver varieties, affine crystals and combinatorics of Auslander-Reiten quivers. https://arxiv.org/abs/1910.07411

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