Representations of Khovanov–Lauda–Rouquier algebras and combinatorics of Lyndon words
Identifieur interne : 000383 ( Main/Exploration ); précédent : 000382; suivant : 000384Representations of Khovanov–Lauda–Rouquier algebras and combinatorics of Lyndon words
Auteurs : Alexander Kleshchev [États-Unis] ; Arun Ram [Australie, États-Unis]Source :
- Mathematische Annalen [ 0025-5831 ] ; 2011-04-01.
Abstract
Abstract: We construct irreducible representations of affine Khovanov–Lauda–Rouquier algebras of arbitrary finite type. The irreducible representations arise as simple heads of appropriate induced modules, and thus our construction is similar to that of Bernstein and Zelevinsky for affine Hecke algebras of type A. The highest weights of irreducible modules are given by the so-called good words, and the highest weights of the ‘cuspidal modules’ are given by the good Lyndon words. In a sense, this has been predicted by Leclerc.
Url:
DOI: 10.1007/s00208-010-0543-1
Affiliations:
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Ann.</title><idno type="ISSN">0025-5831</idno><idno type="eISSN">1432-1807</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>Berlin/Heidelberg</pubPlace><date type="published" when="2011-04-01">2011-04-01</date><biblScope unit="volume">349</biblScope><biblScope unit="issue">4</biblScope><biblScope unit="page" from="943">943</biblScope><biblScope unit="page" to="975">975</biblScope></imprint><idno type="ISSN">0025-5831</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0025-5831</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We construct irreducible representations of affine Khovanov–Lauda–Rouquier algebras of arbitrary finite type. The irreducible representations arise as simple heads of appropriate induced modules, and thus our construction is similar to that of Bernstein and Zelevinsky for affine Hecke algebras of type A. The highest weights of irreducible modules are given by the so-called good words, and the highest weights of the ‘cuspidal modules’ are given by the good Lyndon words. 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