36 citations · 196 across the 42 of their papers we have counts for
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Construction of Irreducible Representations over Khovanov-Lauda-Rouquier Algebras of Finite Classical Type
Georgia Benkart, Seok-Jin Kang, Se-jin Oh +1
We give an explicit construction of irreducible modules over Khovanov-Lauda-Rouquier algebras and their cyclotomic quotients for finite classical types using a crystal ba…
New Irreducible Modules for Heisenberg and Affine Lie Algebras
Viktor Bekkert, Georgia Benkart, Vyacheslav Futorny +1
We study -graded modules of nonzero level with arbitrary weight multiplicities over Heisenberg Lie algebras and the associated generalized loop modules over affine Kac-M…
Hopf algebras with triality
Georgia Benkart, Sara Madariaga, José M. Pérez-Izquierdo
In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping alge…
Motzkin Algebras
Georgia Benkart, Tom Halverson
We introduce an associative algebra $\M_k(x)$ whose dimension is the -th Motzkin number. The algebra $\M_k(x)$ has a basis of "Motzkin diagrams," which are analogous to Brauer…
Lie Algebras with Prescribed sl3 Decomposition
Georgia Benkart, Alberto Elduque
In this work, we consider Lie algebras L containing a subalgebra isomorphic to sl3 and such that L decomposes as a module for that sl3 subalgebra into copies of the adjoint module,…