Questions tagged [klr-algebras]

Questions about the Khovanov-Lauda-Rouquier algebras. These algebras are used in particular to categorify the representations of universal enveloping algebras of semi-simple Lie algebras

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On the order of the head of product of two simple modules over Quiver Hecke Algebras

My question is: We assume the underlying quiver is a Dynkin quiver. Let $L(\lambda)$ and $L(\mu)$ be two simple modules over Quiver Hecke algebra $R$ where $\lambda$ and $\mu$ are two Konstant ...
Yingjin Bi's user avatar
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Homogenous Hermitian form on the KLR algebra

Does there exist a homogenous conjugate-linear automorphism of the KLR algebra? I want to be able to define a homogenous Hermitian form on the (Specht) modules of the (cyclotomic) KLR algebra.
Chris Bowman's user avatar
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Trace on a KLR algebra

The cyclotomic KLR algebra is isomorphic to the Ariki-Koike algebra over a field and so admits a trace (this is used in Hu-Mathas' paper to define bases for the KLR algebra corresponding to Murphy and ...
Chris Bowman's user avatar
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2 votes
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Signs in relations of Brundan--Kleshchev versus Khovanov--Lauda

The following relations in the definition of the quiver Hecke algebra in Brundan--Kleshchev's paper are $$ y_r \psi_r e(\underline{i}) =(\psi_r y_{r+1} - \delta_{i_r,i_{r+1}})e(\underline{i});\\ $$ ...
Chris Bowman's user avatar
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14 votes
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Where does the canonical basis differ from the KLR basis?

The question implicitly asked in Ben Webster's question is: Does the canonical basis of Uq(n+) agree with the basis coming from categorification via Khovanov-Lauda-Rouqier algebras? Thanks to ...
Peter McNamara's user avatar
1 vote
1 answer

Are cyclotomic Khovanov-Lauda-Rouquier algebras symmetric?

Recall that for k a field, a finite dimensional k-algebra A is called symmetric if it is isomorphic to its dual as a bimodule of itself. Which is to say, there's a trace map t:A -> k such that t(...
Ben Webster's user avatar
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