Explicit Pieri Inclusions

By the Pieri rule, the tensor product of an exterior power and a finite-dimensional irreducible representation of a general linear group has a multiplicity-free decomposition. The embeddings of the constituents  are called Pieri inclusions and were first studied by Weyman in his thesis and described...

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Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 28; no. 3
Main Authors Hunziker, Markus, Miller, John A., Sepanski, Mark
Format Journal Article
LanguageEnglish
Published 10.09.2021
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Summary:By the Pieri rule, the tensor product of an exterior power and a finite-dimensional irreducible representation of a general linear group has a multiplicity-free decomposition. The embeddings of the constituents  are called Pieri inclusions and were first studied by Weyman in his thesis and described explicitly by Olver. More recently, these maps have appeared in the work of Eisenbud, Fløystad, and Weyman and of Sam and Weyman to compute pure free resolutions for classical groups. In this paper, we give a new closed form, non-recursive description of Pieri inclusions. For partitions with a bounded number of distinct parts, the resulting algorithm has polynomial time complexity whereas the previously known algorithm has exponential time complexity.
ISSN:1077-8926
1077-8926
DOI:10.37236/9216