Cristian Lenart

Skew Schubert

Cristian Lenart, Schubert Calculus Beyond K-Theory

Modern Schubert calculus has been mostly concerned with the study of the cohomology andK-theory (including their equivariant and quantum generalizations) of flag manifolds. The basic results for other cohomology theories have only been obtained recently; additional complexity is due to the dependence of the geometrically defined classes on reduced words for the corresponding Weyl group elements...

On the Combinatorics of Crystal Graphs, Ii. the Crystal Commutor

We present an explicit combinatorial realization of the commutor in the category of crystals which was first studied by Henriques and Kamnitzer. Our realization is based on certain local moves defined by van Leeuwen.

Hall-littlewood Polynomials, Alcove Walks, and Fillings of Young Diagrams, Ii

In the theory of Hall-Littlewood polynomials in type A, the Hauglund, Haiman, and Loehr formula for Q polynomials and the Schwer formula for P polynomials are related in the previous paper by a compression formula in the special case of regular weights λ. After grouping terms in the Schwer formula the compression formula gives the sum of terms in each group to be a term in the HaglundHaiman-Loe...

A Combinatorial Model for Crystals of Kac-moody Algebras

We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model. We describe crystal graphs and give a LittlewoodRichardson rule for decomposing tensor products of irreducible representations. The new model is based on the ...