Canonical bases for Fock spaces and tensor products

We relate the canonical basis of the Fock space representation of the quantum affine algebra Uq(glˆn), as defined by Leclerc and Thibon [15], to the canonical basis of its restriction to Uq(sln), regarded as a based module in the sense of Lusztig. More generally we consider the restriction to any Le...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2016-10, Vol.302, p.159-189, Article 159
Main Authors: Chuang, Joseph, Tan, Kai Meng
Format: Article
Language:English
Subjects:
Canonical basis
Decomposition numbers
Fock space
Schur algebra
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Summary:We relate the canonical basis of the Fock space representation of the quantum affine algebra Uq(glˆn), as defined by Leclerc and Thibon [15], to the canonical basis of its restriction to Uq(sln), regarded as a based module in the sense of Lusztig. More generally we consider the restriction to any Levi subalgebra. We deduce results on decomposition numbers and branching coefficients of Schur algebras over fields of positive characteristic, generalizing those of Kleshchev [13] and of Tan and Teo [19].
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2016.07.008