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Schubert Polynomial Analogues for Degenerate Involutions

  • Michael JoyceEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 277)

Abstract

We survey the recent study of involution Schubert polynomials and a modest generalization that we call degenerate involution Schubert polynomials. We cite several conditions when (degenerate) involution Schubert polynomials have simple factorization formulae. Such polynomials can be computed by traversing through chains in certain weak order posets, and we provide explicit descriptions of such chains in weak order for involutions and degenerate involutions. As an application, we give several examples of how certain multiplicity-free sums of Schubert polynomials factor completely into very simple linear factors.

Keywords

Schubert polynomial Involution Degenerate involution Weak order Symmetric subgroup 

Notes

Acknowledgements

The author is grateful to Mahir Can for many helpful discussions. The author thanks the referee for their thorough reading of the paper and their helpful suggestions for improvement.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Mathematics DepartmentTulane UniversityNew OrleansUSA

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