Nonrecursive canonical basis computations for low rank Kashiwara crystals of type \(A\)

DOI10.1216/rmj.2022.52.1929OpenAlexW3045961068MaRDI QIDQ2678271

Ola Amara-Omari, Mary Elizabeth Schaps

Publication date: 9 January 2023

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.14650

zbMATH Keywords

multipartitionscanonical basisKashiwara crystals

Mathematics Subject Classification ID

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

Related Items (1)

External vertices for crystals of affine type A

Uses Software

• SageMath

Cites Work

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• A non-recursive criterion for weights of a highest-weight module for an affine Lie algebra
• Weights of multipartitions and representations of Ariki-Koike algebras.
• An LLT-type algorithm for computing higher-level canonical bases
• The crystal base and Littelmann's refined Demazure character formula
• Paths and root operators in representation theory
• Hecke algebras at roots of unity and crystal bases of quantum affine algebras
• Unidirectional Littelmann paths for crystals of type \(A\) and rank 2
• Derived equivalences for symmetric groups and \(\mathfrak{sl}_2\)-categorification.
• On the tensor product of two basic representations of \(U_v(\hat s l_e)\)
• Representation theory of symmetric groups and related Hecke algebras
• Maximal Strings in the Crystal Graph of Spin Representations of the Symmetric and Alternating Groups

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