A Pieri-type formula for the K-theory of a flag manifold

Details A Pieri-type formula for the K-theory of a flag manifold A Pieri-type formula for the K-theory of a flag manifold

2004-07-23

arxiv.org/abs/math/0407412v5

Trans. Amer. Math. Soc. 359 (2007), 2317--2342.

Mathematics

Combinatorics

25 pages, Fixed proof in Lemma 2.17

Scientific paper

We derive explicit Pieri-type multiplication formulas in the Grothendieck ring of a flag variety. These expand the product of an arbitrary Schubert class and a special Schubert class in the basis of Schubert classes. These special Schubert classes are indexed by a cycle which has either the form (k-p+1,k-p+2,...,k+1) or the form (k+p,k+p-1,...,k), and are pulled back from a Grassmannian projection. Our formulas are in terms of certain labeled chains in the k-Bruhat order on the symmetric group and are combinatorial in that they involve no cancellations. We also show that the multiplicities in the Pieri formula are naturally certain binomial coefficients.

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