TY - JOUR
TI - The Leibniz formula for divided difference operators associated to Kac-Moody root systems
DO - https://doi.org/doi:10.7282/T3NG4NZR
PY - 2014
AB - In this dissertation we present a new Leibniz formula (i.e. generalized product rule) for the type of divided difference operators first introduced by Bernšteĭn, Gel'fand, and Gel'fand. The formula applies for divided difference operators associated to the geometric representation of the Coxeter system of any Kac-Moody group, be it finite-dimensional or infinite-dimensional. Our formula shows that in order to study the structure of the equivariant cohomology ring there is no need to actually construct it at all because the structure constants are encoded in our Leibniz formula for divided difference operators. The formula may be used to compute the structure constants and prove general results about them. In the future our results may be useful in finding Littlewood-Richardson rules in equivariant cohomology and may make the study of certain problems in Schubert calculus more accessible to researchers who are not necessarily well-versed in algebro-geometric or topological methods.
KW - Mathematics
KW - Root systems (Algebra)
KW - Difference operators
LA - eng
ER -