arXiv Analytics

Sign in

arXiv:1003.5019 [math.RT]AbstractReferencesReviewsResources

Lectures on geometric realizations of crystals

Alistair Savage

Published 2010-03-25Version 1

These are notes for a lecture series given at the Fields Institute Summer School in Geometric Representation Theory and Extended Affine Lie Algebras, held at the University of Ottawa in June 2009. We give an introduction to the geometric realization of crystal graphs via the quiver varieties of Lusztig and Nakajima. The emphasis is on motivating the constructions through concrete examples. The relation between the geometric construction of crystals and combinatorial realizations using Young tableaux is also discussed.

Comments: 29 pages
Journal: Fields Institute Communications 59, Amer. Math. Soc., Providence, RI, 2011, pp. 45-70
Categories: math.RT, math.AG, math.QA
Subjects: 17B37
Related articles: Most relevant | Search more
arXiv:1007.5384 [math.RT] (Published 2010-07-30, updated 2012-09-18)
A geometric realization of modified quantum algebras
arXiv:1202.1622 [math.RT] (Published 2012-02-08, updated 2012-10-22)
Geometric realization of Khovanov-Lauda-Rouquier algebras associated with Borcherds-Cartan data
arXiv:2312.10582 [math.RT] (Published 2023-12-17)
A geometric realization of the asymptotic affine Hecke algebra

Links

Toolbox