Geodesic
Extremal rays of the equivariant Littlewood-Richardson cone
Joshua Kiers1
1Ohio State University
The electronic journal of combinatorics, Tome 29 (2022) no. 3
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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.
DOI : 10.37236/10569
Classification : 15A42, 15B48, 15B57, 15A18, 52A40, 14M15, 05E14, 14F43, 14N15, 57R91
Mots-clés : Horn's conjecture, Hermitian matrices, extremal rays, equivariant Littlewood-Richardson cone

Joshua Kiers  1

1 Ohio State University 
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     author = {Joshua Kiers},
     title = {Extremal rays of the equivariant {Littlewood-Richardson} cone},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
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     doi = {10.37236/10569},
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Joshua Kiers. Extremal rays of the equivariant Littlewood-Richardson cone. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10569

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