Geodesic
The ABC's of affine Grassmannians and Hall-Littlewood polynomials
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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We give a new description of the Pieri rule for $k$-Schur functions using the Bruhat order on the affine type-$A$ Weyl group. In doing so, we prove a new combinatorial formula for representatives of the Schubert classes for the cohomology of affine Grassmannians. We show how new combinatorics involved in our formulas gives the Kostka-Foulkes polynomials and discuss how this can be applied to study the transition matrices between Hall-Littlewood and $k$-Schur functions. 
@article{DMTCS_2012_special_263_a81,
     author = {Dalal, Avinash J. and Morse, Jennifer},
     title = {The {ABC's} of affine {Grassmannians} and {Hall-Littlewood} polynomials},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3095},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3095/}
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Dalal, Avinash J.; Morse, Jennifer. The ABC's of affine Grassmannians and Hall-Littlewood polynomials. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3095. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3095/

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