Equivariant Cohomology, Schubert Calculus, and Edge Labeled Tableaux

Robichaux, Colleen; Yadav, Harshit; Yong, Alexander

doi:10.1017/9781108877855.010

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Introduction1

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2022

2024

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Cited by 2 publications

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“…In this work we collide the two worlds of [3] and [1] in order to answer a question of C. Robichaux, H. Yadav, and A. Yong [14]. In [3], P. Belkale introduced an algorithm for finding the extremal rays of the Hermitian eigencone (also called the tensor cone or Littlewood-Richardson cone) -the pointed rational cone which among other things governs the nonvanishing of Littlewood-Richardson coefficients.…”

Section: Introductionmentioning

confidence: 99%

Extremal Rays of the Equivariant Littlewood-Richardson Cone

Kiers

2022

Electron. J. Combin.

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We give an inductive procedure for finding the extremal rays of the equivariant Littlewood-Richardson cone, which is closely related to the solution space to S. Friedland's majorized Hermitian eigenvalue problem. In so doing, we solve the "rational version" of a problem posed by C. Robichaux, H. Yadav, and A. Yong. Our procedure is a natural extension of P. Belkale's algorithm for the classical Littlewood-Richardson cone. The main tools for accommodating the equivariant setting are certain foundational results of D. Anderson, E. Richmond, and A. Yong. We also study two families of special rays of the cone and make observations about the Hilbert basis of the associated lattice semigroup.

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