Mirković–Vilonen basis in type 𝐴₁

DOI10.1090/ert/582OpenAlexW3203312769MaRDI QIDQ5158165

Pierre Baumann, Arnaud Demarais

Publication date: 21 October 2021

Published in: Representation Theory of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.01278

zbMATH Keywords

dual canonical basisMirković-Vilonen basis

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Grassmannians, Schubert varieties, flag manifolds (14M15) Semisimple Lie groups and their representations (22E46) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Geometric Langlands program: representation-theoretic aspects (22E57)

Cites Work

• Geometry of canonical bases and mirror symmetry
• Global crystal bases of quantum groups
• Canonical bases in tensor products and graphical calculus for \(U_ q(sl_ 2)\)
• LS galleries, the path model, and MV cycles
• Crystals via the affine Grassmannian
• Geometric Langlands duality and representations of algebraic groups over commutative rings
• Canonical Bases Arising from Quantized Enveloping Algebras
• Preprojective algebras and cluster algebras
• Buildings, spiders, and geometric Satake
• Semicanonical bases and preprojective algebras
• Introduction to quantum groups
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