Noncommutative LR coefficients and crystal reflection operators

DOI10.5802/alco.155zbMath1460.05192arXiv1905.10942OpenAlexW3129945215MaRDI QIDQ2660381

Edward Richmond, Vasu V. Tewari

Publication date: 30 March 2021

Published in: Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.10942

zbMATH Keywords

Littlewood-Richardson coefficientsymmetric functionSchur functionnoncommutative symmetric functioncrystal operator

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Polynomials defined by tableaux and linear recurrences
• Combinatorics and geometry of Littlewood-Richardson cones
• Quasisymmetric Schur functions
• Skew quasisymmetric Schur functions and noncommutative Schur functions
• A Murnaghan-Nakayama rule for noncommutative Schur functions
• A geometric Littlewood-Richardson rule
• Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions
• An algorithmic Littlewood-Richardson rule
• An explicit construction of type A Demazure atoms
• On Schensted's construction and the multiplication of Schur functions
• A Littlewood-Richardson miscellany
• Key polynomials and a flagged Littlewood-Richardson rule
• A simple proof of the Littlewood-Richardson rule and applications.
• The saturation conjecture (after A. Knutson and T. Tao). With an appendix by William Fulton
• Kohnert tableaux and a lifting of quasi-Schur functions
• Dual immaculate quasisymmetric functions expand positively into Young quasisymmetric Schur functions
• Noncommutative symmetric functions
• Plactification
• Schur operators and Knuth correspondences
• Duality between quasi-symmetric functions and the Solomon descent algebra
• Backward jeu de taquin slides for composition tableaux and a noncommutative Pieri rule
• \(K\)-theoretic polynomials
• Crystal Bases
• Skew Littlewood-Richardson Rules from Hopf Algebras
• La correspondance de Robinson
• The honeycomb model of $GL_n(\mathbb C)$ tensor products I: Proof of the saturation conjecture
• An Introduction to Quasisymmetric Schur Functions
• Polynomial bases: Positivity and Schur multiplication
• A Lift of the Schur and Hall–Littlewood Bases to Non-commutative Symmetric Functions