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.
@article{10_37236_9216,
author = {Markus Hunziker and John A. Miller and Mark Sepanski},
title = {Explicit {Pieri} inclusions},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {3},
doi = {10.37236/9216},
zbl = {1472.13025},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9216/}
}
TY - JOUR
AU - Markus Hunziker
AU - John A. Miller
AU - Mark Sepanski
TI - Explicit Pieri inclusions
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/9216/
DO - 10.37236/9216
ID - 10_37236_9216
ER -
%0 Journal Article
%A Markus Hunziker
%A John A. Miller
%A Mark Sepanski
%T Explicit Pieri inclusions
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/9216/
%R 10.37236/9216
%F 10_37236_9216
Markus Hunziker; John A. Miller; Mark Sepanski. Explicit Pieri inclusions. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/9216
