Séminaire Lotharingien de Combinatoire, 91B.47 (2024), 11 pp.
Daoji Huang and Son Nguyen
Growth Diagrams for Schubert RSK
Abstract.
Motivated by classical combinatorial Schubert calculus on the Grassmannian, Huang and Pylyavskyy introduced a generalized theory of Robinson-Schensted-Knuth (RSK) correspondence for studying Schubert calculus on the complete flag variety, via insertion algorithms. The inputs of the correspondence are certain biwords, the insertion objects are bumpless pipe dreams, and the recording objects are certain chains in Bruhat order. In particular, they defined plactic biwords and showed that classical Knuth relations can be generalized to these. In this extended abstract, we give an analogue of Fomin's growth diagrams for this generalized RSK correspondence on plactic biwords. We show that this growth diagram recovers the bijection between pipe dreams and bumpless pipe dreams of Gao and Huang.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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