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Homomorphisms between standard modules over finite-type KLR algebras

Part of: Lie algebras and Lie superalgebras Representation theory of rings and algebras Homological methods

Published online by Cambridge University Press:  01 March 2017

Alexander S. Kleshchev  and
David J. Steinberg
Alexander S. Kleshchev
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, USA email [email protected]
David J. Steinberg
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, USA email [email protected]
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Abstract

Khovanov–Lauda–Rouquier (KLR) algebras of finite Lie type come with families of standard modules, which under the Khovanov–Lauda–Rouquier categorification correspond to PBW bases of the positive part of the corresponding quantized enveloping algebra. We show that there are no non-zero homomorphisms between distinct standard modules and that all non-zero endomorphisms of a standard module are injective. We present applications to the extensions between standard modules and modular representation theory of KLR algebras.

Keywords

representations of Khovanov–Lauda–Rouquier algebrascategorificationaffine quasihereditary algebras

MSC classification

Primary: 16G99: None of the above, but in this section 16E05: Syzygies, resolutions, complexes 17B37: Quantum groups (quantized enveloping algebras) and related deformations
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 3 , March 2017 , pp. 621 - 646
Copyright
© The Authors 2017 

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