Georgia Benkart

Learn More
The algebra generated by the down and up operators on a diierential partially ordered set (poset) encodes essential enumerative and structural properties of the poset. Motivated by the algebras generated by the down and up operators on posets, we introduce here a family of innnite-dimensional associative algebras called down-up algebras. We show that(More)
We deene and characterize switching, an operation that takes two tableaux sharing a common border and \moves them through each other" giving another such pair. Several authors, including James and Kerber, Remmel, Haiman, and Shimozono, have deened switching operations; however, each of their operations is somewhat diierent from the rest and each imposes a(More)
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 complete reducibility result. These quantum groups have a natural n-dimensional module V. We prove an analogue of Schur-Weyl duality in this setting: the centralizer algebra of the(More)
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 Drinfel'd doubles of certain Hopf subalgebras with respect to Hopf pairings. Using the Hopf pairing, we construct a corresponding R-matrix. The quantum groups have a natural(More)
To subscribe to email notification of new AMS publications, please go to Contents: Graded Lie algebras; Simple Lie algebras and algebraic groups; The contragredient case; The noncontragredient case; Bibliography. This volume contains fourteen cutting-edge research articles on algebraic and analytic aspects of singularities of spaces and maps. By reading(More)