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Subregular representations of $\mathfrak {sl}_n$ and simple singularities of type $A_{n-1}$. II

Authors: Iain Gordon and Dmitriy Rumynin
Journal: Represent. Theory 8 (2004), 328-345
MSC (2000): Primary 17B50; Secondary 14J17, 16S35, 18F25, 20G05
Published electronically: July 20, 2004
MathSciNet review: 2077485
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Abstract: The aim of this paper is to show that the structures on $K$-theory used to formulate Lusztig’s conjecture for subregular nilpotent $\mathfrak {sl}_n$-representations are, in fact, natural in the McKay correspondence. The main result is a categorification of these structures. The no-cycle algebra plays the special role of a bridge between complex geometry and representation theory in positive characteristic.

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Additional Information

Iain Gordon
Affiliation: Department of Mathematics, University of Glasgow, Glasgow, G12 8QW, United Kingdom

Dmitriy Rumynin
Affiliation: Department of Mathematics, University of Warwick, Coventry, CV4 7AL, United Kingdom

Received by editor(s): January 22, 2003
Received by editor(s) in revised form: February 12, 2004
Published electronically: July 20, 2004
Additional Notes: Both authors were visiting and partially supported by MSRI while this research was begun and extend their thanks to that institution. Much of the research for this paper was undertaken while the first author was supported by TMR grant ERB FMRX-CT97-0100 at the University of Bielefeld and Nuffield grant NAL/00625/G
The second author was partially supported by EPSRC
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.