Geometric and Combinatorial Realizations of Crystals of Enveloping Algebras

Details Geometric and Combinatorial Realizations of Crystals of Enveloping Algebras Geometric and Combinatorial Realizations of Crystals of Enveloping Algebras

2006-01-20

arxiv.org/abs/math/0601511v1

Lie algebras, vertex operator algebras and their applications (Raleigh, NC, 2005), 221-232, Contemp. Math., 442, Amer. Math. S

Mathematics

Quantum Algebra

12 pages

Scientific paper

Kashiwara and Saito have defined a crystal structure on the set of irreducible components of Lusztig's quiver varieties. This gives a geometric realization of the crystal graph of the lower half of the quantum group associated to a simply-laced Kac-Moody algebra. Using an enumeration of the irreducible components of Lusztig's quiver varieties in finite and affine type A by combinatorial data, we compute the geometrically defined crystal structure in terms of this combinatorics. We conclude by comparing the combinatorial realization of the crystal graph thus obtained with other combinatorial models involving Young tableaux and Young walls.

Affiliated with

Also associated with

No associations

Rating

Geometric and Combinatorial Realizations of Crystals of Enveloping Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometric and Combinatorial Realizations of Crystals of Enveloping Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric and Combinatorial Realizations of Crystals of Enveloping Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-438336