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

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- by Iain Gordon and Dmitriy Rumynin
- Represent. Theory
**8**(2004), 328-345 - DOI: https://doi.org/10.1090/S1088-4165-04-00186-4
- Published electronically: July 20, 2004
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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.## References

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## Bibliographic Information

**Iain Gordon**- Affiliation: Department of Mathematics, University of Glasgow, Glasgow, G12 8QW, United Kingdom
- Email: ig@maths.gla.ac.uk
**Dmitriy Rumynin**- Affiliation: Department of Mathematics, University of Warwick, Coventry, CV4 7AL, United Kingdom
- Email: rumynin@maths.warwick.ac.uk
- 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 - © Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**8**(2004), 328-345 - MSC (2000): Primary 17B50; Secondary 14J17, 16S35, 18F25, 20G05
- DOI: https://doi.org/10.1090/S1088-4165-04-00186-4
- MathSciNet review: 2077485