Crystal energy functions via the charge in types A and C

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Date
2011-05-23MFO Scientific Program
Research in Pairs 2011Series
Oberwolfach Preprints;2011,25Author
Lenart, Cristian
Schilling, Anne
Metadata
Show full item recordOWP-2011-25
Abstract
The Ram-Yip formula for Macdonald polynomials (at $t=0$) provides a statistic which we call charge. In types $A$ and $C$ it can be defined on tensor products of Kashiwara-Nakashima single column crystals. In this paper we prove that the charge is equal to the (negative of the) energy function on affine crystals. The algorithm for computing charge is much simpler and can be more efficiently computed than the recursive definition of energy in terms of the combinatorial $R$-matrix.