KLR algebras and the branching rule I: The categorical Gelfand-Tsetlin basis in type An
(2013) ArXiV — (2013)
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- Abstract
- We define a quotient of the category of finitely generated modules over the cyclotomic Khovanov-Lauda-Rouquier algebra for type An and show it has a module category structure over a direct sum of certain cyclotomic Khovanov-Lauda-Rouquier algebras of type An-1, this way categorifying the branching rules for the inclusion of sl(n) in sl(n+1). Using this we give a new, elementary proof of Khovanov-Lauda cyclotomic conjecture. We show that continuing recursively gives the Gelfand-Tsetlin basis for type An. As an application we prove a conjecture of Mackaay, Stosic and Vaz concerning categorical Weyl modules.
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Citations
Dos Santos Santana Forte Vaz, P. (2013). KLR algebras and the branching rule I: The categorical Gelfand-Tsetlin basis in type An. ArXiV. Submitted. https://hdl.handle.net/2078.5/22664 (Original work published 2013)