Combinatorics of the CasselmanShalika formula in type A
Abstract
In the recent works of BrubakerBumpFriedberg, BumpNakasuji, and others, the product in the CasselmanShalika formula is written as a sum over a crystal. The coefficient of each crystal element is defined using the data coming from the whole crystal graph structure. In this paper, we adopt the tableaux model for the crystal and obtain the same coefficients using data from each individual tableaux; i.e., we do not need to look at the graph structure. We also show how to combine our results with tensor products of crystals to obtain the sum of coefficients for a given weight. The sum is a qpolynomial which exhibits many interesting properties. We use examples to illustrate these properties.
 Publication:

arXiv eprints
 Pub Date:
 November 2011
 DOI:
 10.48550/arXiv.1111.1134
 arXiv:
 arXiv:1111.1134
 Bibcode:
 2011arXiv1111.1134L
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Combinatorics;
 17B37 (Primary) 05E10 (Secondary)
 EPrint:
 10 pages