Date: Friday, December 02, 2011
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: The combinatorics of affine crystals and the energy function
Abstract: Crystals are colored directed graphs encoding information about Lie algebra
representations. Certain (not highest weight) crystals for affine Lie algebras
known as KirillovReshetikhin (KR) crystals are graded by the energy function.
Since crystals have various combinatorial models, it is desirable to compute the
energy as a related statistic. With A. Postnikov we defined the socalled alcove
model for (highest weight) crystals. I will present a generalization which is
conjectured to model tensor products of KR crystals of arbitrary Lie type. The
conjecture implies that a related statistic computes the energy. There is
reasonable evidence for this conjecture. For instance, it is proved for Lie
types A and C (i.e., for the special linear and symplectic algebras). I rephrase
the energy statistic in type A as a wellknown word statistic (the charge),
while in type C I define a similar one. The talk contains joint work with Anne
Schilling and Arthur Lubovsky, and is largely selfcontained.
Files:
Speaker: Cristian Lenart
Institution: SUNY Albany
Event Organizer:
