Séminaire Lotharingien de Combinatoire, 93B.84 (2025), 12 pp.

Santiago Estupiñán-Salamanca and Oliver Pechenik

A New Shifted Littlewood-Richardson Rule and Related Developments

Abstract. As Littlewood-Richardson rules compute linear representation theory of symmetric groups and cohomology of ordinary Grassmannians, shifted Littlewood-Richardson rules compute analogous projective representation theory of symmetric groups and cohomology of orthogonal Grassmannians. The first shifted Littlewood-Richardson rule is due to Stembridge (1989). We give a new shifted Littlewood-Richardson rule that is provably more efficient in some cases and is more convenient for hand calculations. Our rule builds on ideas of Lascoux-Schützenberger (1981), Haiman (1989), and Serrano (2010).


Received: November 15, 2024. Accepted: February 15, 2025. Final version: April 1, 2025.

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