Skew quantum Murnaghan-Nakayama rule

Details Skew quantum Murnaghan-Nakayama rule Skew quantum Murnaghan-Nakayama rule

2011-01-27

arxiv.org/abs/1101.5250v1

Mathematics

Combinatorics

19 pages, 16 figures

Scientific paper

In this paper, we extend recent results of Assaf and McNamara on skew Pieri rule and skew Murnaghan-Nakayama rule to a more general identity, which gives an elegant expansion of the product of a skew Schur function with a quantum power sum function in terms of skew Schur functions. We give two proofs, one completely bijective in the spirit of Assaf-McNamara's original proof, and one via Lam-Lauve-Sotille's skew Littlewood-Richardson rule. We end with some conjectures for skew rules for Hall-Littlewood polynomials.

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