Explicit Pieri Inclusions
| Autor: | Markus Hunziker, John A. Miller, Mark R. Sepanski |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Exponential complexity
Classical group Applied Mathematics General linear group Theoretical Computer Science Combinatorics Tensor product Computational Theory and Mathematics Irreducible representation Bounded function Discrete Mathematics and Combinatorics Geometry and Topology Polynomial time complexity Mathematics |
| Zdroj: | The Electronic Journal of Combinatorics. 28 |
| ISSN: | 1077-8926 |
| DOI: | 10.37236/9216 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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