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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Graded Hecke Algebras for the Symmetric Group in Positive Characteristic

Krawzik, Naomi 08 1900 (has links)
Graded Hecke algebras are deformations of skew group algebras which arise from a group acting on a polynomial ring. Over fields of characteristic zero, these deformations have been studied in depth and include both symplectic reflection algebras and rational Cherednik algebras as examples. In Lusztig's graded affine Hecke algebras, the action of the group is deformed, but not the commutativity of the vectors. In Drinfeld's Hecke algebras, the commutativity of the vectors is deformed, but not the action of the group. Lusztig's algebras are all isomorphic to Drinfeld's algebras in the nonmodular setting. We find new deformations in the modular setting, i.e., when the characteristic of the underlying field divides the order of the group. We use Poincare-Birkhoff-Witt conditions to classify these deformations arising from the symmetric group acting on a polynomial ring in arbitrary characteristic, including the modular case.

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