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Kus, D. and Schumann, B. (2022). Nakajima quiver varieties, affine crystals and combinatorics of Auslander-Reiten quivers. Algebra Discret. Math., 34 (2). S. 244 - 273. Poltava: LUHANSK TARAS SHEVCHENKO NATL UNIV. ISSN 2415-721X

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Abstract

We obtain an explicit crystal isomorphism be-tween two realizations of crystal bases of finite dimensional irre-ducible 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 vari-eties 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kus, D. UNSPECIFIED UNSPECIFIED UNSPECIFIED Schumann, B. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-665074
DOI:	10.12958/adm1952
Journal or Publication Title:	Algebra Discret. Math.
Volume:	34
Number:	2
Page Range:	S. 244 - 273
Date:	2022
Publisher:	LUHANSK TARAS SHEVCHENKO NATL UNIV
Place of Publication:	Poltava
ISSN:	2415-721X
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language BASES Multiple languages Mathematics, Applied Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66507