Explicit Pieri Inclusions

@article{Hunziker2021ExplicitPI,
  title={Explicit Pieri Inclusions},
  author={Markus Hunziker and John G. Miller and Mark Roger Sepanski},
  journal={Electron. J. Comb.},
  year={2021},
  volume={28}
}
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… 

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References

SHOWING 1-10 OF 19 REFERENCES

Pieri resolutions for classical groups

Explicit generalized Pieri maps

Computational Methods for Orbit Closures in a Representation with Finitely Many Orbits

TLDR
Kraśkiewicz and Weyman give a conjectural description of the minimal free resolution of the coordinate ring for certain orbit closures in and verify that they generate radical ideals.

THE EXISTENCE OF EQUIVARIANT PURE FREE

— Let A = K[x1, . . . , xm] be a polynomial ring in m variables and let d = (d0 < · · · < dm) be a strictly increasing sequence of m + 1 integers. Boij and Söderberg conjectured the existence of

ANNALES DE L’INSTITUT FOURIER

. — We show that for a finite-type Lie algebra g , the representation theory of quiver Hecke algebras provides a natural framework for the construction of Newton–Okounkov bodies associated to the

Equations for secant varieties of Veronese and other varieties

New classes of modules of equations for secant varieties of Veronese varieties are defined using representation theory and geometry. Some old modules of equations (catalecticant minors) are revisited

Journal of Software for Algebra and Geometry

TLDR
The package PhylogeneticTrees for Macaulay 2 is introduced, which allows users to compute phylogenetic invariants for group-based tree models and it is shown how methods within the package can be used to compute a generating set for the join of any two ideals.

Koszul-Young Flattenings and Symmetric Border Rank of the Determinant

Representation Theory: A First Course

This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras. Following an introduction to representation