Lectures on geometric realizations of crystals
Alistair Savage
TL;DR
This paper introduces the geometric realization of crystal graphs through quiver varieties, connecting algebraic and combinatorial perspectives with concrete examples and classical tableaux.
Contribution
It provides an accessible introduction to geometric crystal realizations and explores their relation to combinatorial models like Young tableaux.
Findings
Crystal graphs can be realized geometrically via quiver varieties.
The geometric approach is motivated through concrete examples.
Connections between geometric and combinatorial crystal models are discussed.
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics