Affine charge and the \(k\)-bounded Pieri rule. (English. French summary) Zbl 1335.05226
Proceedings of the 27th international conference on formal power series and algebraic combinatorics, FPSAC 2015, Daejeon, South Korea, July 6–10, 2015. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Mathematics and Theoretical Computer Science. Proceedings, 405-416 (2015).
Summary: We provide a new description of the Pieri rule of the homology of the affine Grassmannian and an affine analogue of the charge statistics in terms of bounded partitions. This makes it possible to extend the formulation of the Kostka-Foulkes polynomials in terms of solvable lattice models by A. Nakayashiki and Y. Yamada [Sel. Math., New Ser. 3, No. 4, 547–599 (1997; Zbl 0915.17016)] to the affine setting.
For the entire collection see [Zbl 1333.05004].
For the entire collection see [Zbl 1333.05004].
MSC:
| 05E15 | Combinatorial aspects of groups and algebras (MSC2010) |
| 14N15 | Classical problems, Schubert calculus |
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
