Seminar Event Detail


Combinatorics

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 Kirillov-Reshetikhin (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 so-called 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 well-known 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 self-contained.

Files:


Speaker:  Cristian Lenart
Institution:  SUNY Albany

Event Organizer:     

 

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