G. Benkart

activity

19962020

most citedRepresentations of Two-Parameter Quantum Groups and Schur-Weyl Duality

36 citations · 196 across the 42 of their papers we have counts for

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Showing 1998Show all

4 papers · 1 filter

math.QA1998★ 17 cited

Crystal Bases for the Quantum Superalgebra $U_{q} (g l (m, n))$

Georgia Benkart, Seok-Jin Kang, Masaki Kashiwara

We develop a crystal base theory for the general linear Lie superalgebra $g l (m, n)$ . We prove that any irreducible $U_{q} (g l (m, n))$ -module in some category has a crystal base, and pro…

math.RT1998

The Polynomial Behavior of Weight Multiplicities for the Affine Kac-Moody Algebras $A_{r}^{(1)}$

Georgia Benkart, Seok-Jin Kang, Hyeonmi Lee +2

We prove that the multiplicity of an arbitrary dominant weight for an integrable highest weight representation of the affine Kac-Moody algebra $A_{r}^{(1)}$ is a polynomial in the…

math.RT1998

Down-up Algebras

Georgia Benkart, Tom Roby

The algebra generated by the down and up operators on a differential partially ordered set (poset) encodes essential enumerative and structural properties of the poset. Motivated b…

math.QA1998

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 $U_{q}$ (D $_{4}$ ) of D $_{4}$ , we construct a quantum analogue of the split…

Crystal Bases for the Quantum Superalgebra Uq​(gl(m,n))

The Polynomial Behavior of Weight Multiplicities for the Affine Kac-Moody Algebras Ar(1)​

Down-up Algebras

A quantum octonion algebra

Crystal Bases for the Quantum Superalgebra $U_{q} (g l (m, n))$

The Polynomial Behavior of Weight Multiplicities for the Affine Kac-Moody Algebras $A_{r}^{(1)}$