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A Murgnahan-Nakayama rule for Schubert polynomials

Abstract : We expose a rule for multiplying a general Schubert polynomial with a power sum polynomial in $k$ variables. A signed sum over cyclic permutations replaces the signed sum over rim hooks in the classical Murgnahan-Nakayama rule. In the intersection theory of flag manifolds this computes all intersections of Schubert cycles with tautological classes coming from the Chern character. We also discuss extensions of this rule to small quantum cohomology.
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Andrew Morrison. A Murgnahan-Nakayama rule for Schubert polynomials. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.525-536, ⟨10.46298/dmtcs.2420⟩. ⟨hal-01207549⟩

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