36 citations · 196 across the 42 of their papers we have counts for
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Yetter-Drinfeld modules under cocycle twists
Georgia Benkart, Mariana Pereira, Sarah Witherspoon
We give an explicit formula for the correspondence between simple Yetter-Drinfeld modules for certain finite-dimensional pointed Hopf algebras and those for cocycle twists $H^σ…
Quantum Group Actions, Twisting Elements, and Deformations of Algebras
Georgia Benkart, Sarah Witherspoon
We construct twisting elements for module algebras of restricted two-parameter quantum groups from factors of their R-matrices. We generalize the theory of Giaquinto and Zhang to u…
Irreducible Modules for the Quantum Affine Algebra and its Borel subalgebra
Georgia Benkart, Paul Terwilliger
Let denote the Borel subalgebra of the quantum affine algebra . We show that the following hold for any choice of scalars fro…
Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality
Georgia Benkart, Sarah Witherspoon
We determine the finite-dimensional simple modules for two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl_n and sl_n, and give a co…
Two-Parameter Quantum Groups and Drinfel'd Doubles
Georgia Benkart, Sarah Witherspoon
We investigate two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl_n and sl_n. We show that these quantum groups can be realized as…
Crystal Bases for the Quantum Superalgebra
Georgia Benkart, Seok-Jin Kang, Masaki Kashiwara
We develop a crystal base theory for the general linear Lie superalgebra . We prove that any irreducible -module in some category has a crystal base, and pro…
A quantum octonion algebra
Georgia Benkart, José M. Pérez-Izquierdo
Using the natural irreducible 8-dimensional representation and the two spin representations of the quantum group (D) of D, we construct a quantum analogue of the split…