dc.contributor.author El Fassy Fihry, Youssef en_US dc.date.accessioned 2014-02-25T18:36:46Z dc.date.available 2014-02-25T18:36:46Z dc.date.issued 2014-01-27 en_US dc.identifier.other bibid: 8442395 dc.identifier.uri https://hdl.handle.net/1813/36036 dc.description.abstract Given a finite Coxeter group W acting on its ﬁnite dimensional reﬂection representation V, we consider the ring D(ΩV)[RTIMES]W of equivariant differential operators on differential forms on V. After computing its Hochschild cohomology, we deduce the existence of a universal formal deformation of it, parametrized by the set of conjugation invariant functions on the set of reﬂections of W. We then introduce the graded Cherednik algebra, which represents an algebraic realization of that deformation. Using the deformed de Rham differential introduced by Dunkl and Opdam, we deform the standard Lie derivative operator and construct a Dunkl type embedding for the graded Cherednik algebra which extends the classical one. This embedding allows us to endow the graded Cherednik algebra with a natural differential. We study its cohomology and relate it to the singular polynomials of W. Finally, following the idea in the classical case, we investigate different notions of quasi-invariant differential forms and their relation to the spherical subalgebra of the graded Cherednik algebra. en_US dc.language.iso en_US en_US dc.title Graded Cherednik Algebra And Quasi-Invariant Differential Forms en_US dc.type dissertation or thesis en_US thesis.degree.discipline Mathematics thesis.degree.grantor Cornell University en_US thesis.degree.level Doctor of Philosophy thesis.degree.name Ph. D., Mathematics dc.contributor.chair Berest, Yuri en_US dc.contributor.committeeMember Sjamaar, Reyer en_US dc.contributor.committeeMember Barbasch, Dan Mihai en_US
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