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Algebras and Representation Theory

, Volume 21, Issue 4, pp 859–895 | Cite as

Some Methods of Computing First Extensions Between Modules of Graded Hecke Algebras

Article

Abstract

In this paper, we establish connections between the first extensions of simple modules and certain filtrations of of standard modules in the setting of graded Hecke algebras. The filtrations involved are radical filtrations and Jantzen filtrations. Our approach involves the use of information from the Langlands classification as well as some deeper understanding on some structure of some modules. Such module arises from the image of a Knapp-Stein type intertwining operator and is a quotient of a generalized standard module. As an application, we compute the Ext-groups for irreducible modules in a block for the graded Hecke algebra of type C 3, assuming the truth of a version of Jantzen conjecture.

Keywords

Graded Hecke algebras Extensions Standard modules Filtrations 

Mathematics Subject Classification (2010)

20C08 16E30 22E50 

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Notes

Acknowledgments

The author would like to thank Dan Ciubotaru and Peter Trapa for discussions on Jantzen filtrations and would like to thank Eric Opdam for discussions on intertwining operators. The author would like to thank the referee for useful comments. This research was supported by both of the ERC-advanced grant no. 268105 from Eric Opdam and the Croucher Fellowship.

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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA

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