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FROM COMPLETE TO PARTIAL FLAGS IN GEOMETRIC EXTENSION ALGEBRAS

Part of: Special varieties Representation theory of groups (Co)homology theory

Published online by Cambridge University Press:  13 March 2017

JULIA SAUTER
JULIA SAUTER*
Affiliation:
Faculty of Mathematics, Bielefeld University, PO Box 100 131, 33501 Bielefeld, Germany e-mail: jsauter@math.uni-bielefeld.de
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Abstract

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A geometric extension algebra is an extension algebra of a semi-simple perverse sheaf (allowing shifts), e.g., a push-forward of the constant sheaf under a projective map. Particular nice situations arise for collapsings of homogeneous vector bundles over homogeneous spaces. In this paper, we study the relationship between partial flag and complete flag cases. Our main result is that the locally finite modules over the geometric extension algebras are related by a recollement. As examples, we investigate parabolic affine nil Hecke algebras, geometric extension algebras associated with parabolic Springer maps and an example of Reineke of a parabolic quiver-graded Hecke algebra.

MSC classification

Primary: 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
Secondary: 20C08: Hecke algebras and their representations 14M99: None of the above, but in this section 14F05: Sheaves, derived categories of sheaves and related constructions
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 1 , January 2018 , pp. 111 - 121
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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