Combinatorics of canonical bases revisited: type A

DOI10.1007/s00029-021-00658-xOpenAlexW3180806760MaRDI QIDQ2046897

Bea Schumann, Volker Genz, Gleb A. Koshevoy

Publication date: 19 August 2021

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.03465

zbMATH Keywords

double Bruhat cellscluster algebrascrystal basesMV-polytopesrhombic tilingsBerenstein-Kazhdan potentialGross-Hacking-Keel-Kontsevich potentialLusztig's parametrizationstring parametrization

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (7)

Crystal structures on FFLV polytopes ⋮ An algorithm for Berenstein-Kazhdan decoration functions and trails for minuscule representations ⋮ Combinatorics of canonical bases revisited: string data in type \textsf{A} ⋮ Polyhedral realizations for \(B(\infty)\) and extended Young diagrams, Young walls of type \(\mathrm{A}^{(1)}_{n-1}\), \(\mathrm{C}^{(1)}_{n-1}\), \(\mathrm{A}^{(2)}_{2n-2}\), \(\mathrm{D}^{(2)}_n\) ⋮ Polyhedral realizations for crystal bases of integrable highest weight modules and combinatorial objects of type \(\mathrm{A}^{(1)}_{n-1}, \mathrm{C}^{(1)}_{n-1}, \mathrm{A}^{(2)}_{2n-2}, \mathrm{D}^{(2)}_n\) ⋮ Cluster decorated geometric crystals, generalized geometric RSK-correspondences, and Donaldson-Thomas transformations ⋮ Redundancy in string cone inequalities and multiplicities in potential functions on cluster varieties

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