The Pelletier-Ressayre hidden symmetry for Littlewood-Richardson coefficients

Abstract

We prove an identity for Littlewood--Richardson coefficients conjectured by Pelletier and Ressayre (arXiv:2005.09877). The proof relies on a novel birational involution defined over any semifield.

86 pages. Reproves some basic properties of Schur Laurent polynomials (with negative parts) that I could not find in the literature. The birational map studied in Section 3 might be useful elsewhere. Detailed version available as ancillary file. v5 adds one proof in §5.2.2 and two in §5.4 (all in the detailed version only) and fixes a missing reference. Comments are welcome!

References in corpus (2)

• The Pelletier-Ressayre hidden symmetry for Littlewood-Richardson coefficients
• The 144 symmetries of the Littlewood-Richardson coefficients of $S{L}_3$

Cited by in corpus (3)

• The Pelletier-Ressayre hidden symmetry for Littlewood-Richardson coefficients
• Partial symmetries of iterated plethysms
• Even-carry polynomials and cohomology of line bundles on the incidence correspondence in positive characteristic