Affine PBW bases and affine MV polytopes

DOI10.1007/s00029-018-0436-9zbMath1459.17032arXiv1609.06613OpenAlexW2523662059WikidataQ129253179 ScholiaQ129253179MaRDI QIDQ1618284

Dinakar Muthiah, Peter Tingley

Publication date: 13 November 2018

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

Full work available at URL: https://arxiv.org/abs/1609.06613

zbMATH Keywords

quantum affine algebracrystalPBW basisaffine MV polytope

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

Related Items

Diagram automorphisms and canonical bases for quantum affine algebras, Unnamed Item, Diagram automorphisms and canonical bases for quantum affine algebras. II

Cites Work

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• Affine Mirković-Vilonen polytopes
• Crystal bases and two-sided cells of quantum affine algebras
• Mirković-Vilonen cycles and polytopes.
• PBW basis of quantized universal enveloping algebras
• Braid group action and quantum affine algebras
• Convex bases of PBW type for quantum affine algebras
• Geometric construction of crystal bases
• A polytope calculus for semisimple groups.
• Dual canonical bases, quantum shuffles and \(q\)-characters
• Tensor product multiplicities, canonical and totally positive varieties
• An integral PBW basis of the quantum affine algebra of type \(A_2^{(2)}\).
• An algebraic characterization of the affine canonical basis
• The crystal structure on the set of Mirković-Vilonen polytopes
• Representations of Khovanov-Lauda-Rouquier algebras. III: Symmetric affine type
• Affine PBW bases and MV polytopes in rank 2
• Geometric Langlands duality and representations of algebraic groups over commutative rings
• Braid group action and canonical bases
• The R-matrix for (twisted) affine quantum algebras
• THE CLASSIFICATION OF CONVEX ORDERS ON AFFINE ROOT SYSTEMS
• Preprojective algebras and MV polytopes
• Rank 2 affine MV polytopes
• Canonical Bases Arising from Quantized Enveloping Algebras
• On Mirković-Vilonen cycles and crystal combinatorics
• Quivers, Perverse Sheaves, and Quantized Enveloping Algebras
• Elementary construction of Lusztig’s canonical basis
• Mirkovic-Vilonen polytopes and Khovanov-Lauda-Rouquier algebras