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5 - The Springer Correspondence

Published online by Cambridge University Press:  25 November 2023

Edited by
David Jordan ,
Nadia Mazza  and
Sibylle Schroll
David Jordan
Affiliation:
University of Edinburgh
Nadia Mazza
Affiliation:
Lancaster University
Sibylle Schroll
Affiliation:
Universität zu Köln
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Summary

We present some key concepts and tools in the field of geometric representation theory. We review the background necessary to state the Springer correspondence for an arbitrary semisimple Lie algebra. We then study the notion of convolution in Borel–Moore homology and see how to apply it to the Springer correspondence. Finally, we reframe these ideas in the language of perverse sheaves and intersection homology.

Keywords

geometric representation theorySpringer correspondenceBorel–Moore homologyperverse sheaves
Type
Chapter
Information
Modern Trends in Algebra and Representation Theory , pp. 169 - 211
Publisher: Cambridge University Press
Print publication year: 2023

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