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arXiv · 1403.0607

A Murnaghan-Nakayama Rule For Noncommutative Schur Functions

Vasu V. Tewari
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Abstract

We prove a Murnaghan-Nakayama rule for the noncommutative Schur functions introduced by Bessenrodt, Luoto and van Willigenburg. In other words, we give an explicit combinatorial formula for expanding the product of a noncommutative power sum symmetric function and a noncommutative Schur function in terms of noncommutative Schur functions. In direct analogy to the classical Murnaghan-Nakayama rule, the summands are computed using a noncommutative analogue of border strips, and have coefficients equal to 1 or -1 determined by the height of these border strips. The rule is proved by interpreting the noncommutative Pieri rules for noncommutative Schur functions in terms of box-adding operators on compositions.

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Vasu V. Tewari. 2014-03-03. A Murnaghan-Nakayama Rule For Noncommutative Schur Functions. https://arxiv.org/abs/1403.0607

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