Subregular Nilpotent Elements and Bases in $K$ -Theory
Canadian journal of mathematics, Tome 51 (1999) no. 6, pp. 1194-1225

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we describe a canonical basis for the equivariant $K$ -theory (with respect to a ${{\mathbf{C}}^{*}}$ -action) of the variety of Borel subalgebras containing a subregular nilpotent element of a simple complex Lie algebra of type $D$ or $E$ .
DOI : 10.4153/CJM-1999-053-1
Mots-clés : 20G99
Lusztig, G. Subregular Nilpotent Elements and Bases in $K$ -Theory. Canadian journal of mathematics, Tome 51 (1999) no. 6, pp. 1194-1225. doi: 10.4153/CJM-1999-053-1
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[B] [B] Brieskorn, E., Singular elements of semisimple algebraic groups, Actes Congrès Intern. Math. 2(1970), 279–284. Google Scholar

[C] [C] Coxeter, H. S. M., The product of generators of a finite group generated by reflections, Duke Math. J. 18(1951), 765–782. Google Scholar

[GV] [GV] Gonzales-Sprinberg, G. and Verdier, J.-L., Construction géométrique de la correspondance de McKay, Ann. Sci. École Norm. Sup. 16(1983), 409–449. Google Scholar

[IN] [IN] Ito, Y. and Nakamura, I., McKay correspondence and Hilbert schemes. Proc. Japan Acad. Ser. A Math. Sci. 72(1996), 135–138. Google Scholar

[KL] [KL] Kazhdan, D. and Lusztig, G., Proof of the Deligne-Langlands conjecture for Hecke algebras. Invent. Math. 53(1979), 153–215. Google Scholar

[Kr] [Kr] Kronheimer, P. B., The construction of ALE spaces as hyper-Kähler quotients. J. Differential Geom. 29(1989), 665–683. Google Scholar

[L1] [L1] Lusztig, G., Some examples of square integrable representations of semisimple p-adic groups. Trans. Amer. Math. Soc. 277(1983), 623–653. Google Scholar

[L2] [L2] Lusztig, G., Quivers, perverse sheaves and quantized enveloping algebras. J. Amer.Math. Soc. 4(1991), 365–421. Google Scholar

[L3] [L3] Lusztig, G., On quiver varieties. Adv. inMath. 136(1988), 141–182. Google Scholar

[L4] [L4] Lusztig, G., Bases in equivariant K-theory. Represent. Th. (electronic) 2(1998), 298–369. Google Scholar

[L5] [L5] Lusztig, G., Bases in equivariant K-theory, II. Represent. Th. (electronic) 3(1999), 281–353. Google Scholar

[M] [M] McKay, J., Graphs, singularities and finite groups. Proc. Sympos. Pure Math. 37(1980), 183–186. Google Scholar

[N1] [N1] Nakajima, H., Instantons on ALE spaces, quiver varieties and Kac-Moody algebras. DukeMath. J. 76(1994), 365–416. Google Scholar

[N2] [N2] Nakajima, H., Lectures on Hilbert schemes of points on surfaces. (1996). Google Scholar

[S] [S] Slodowy, P. Simple algebraic groups and simple singularities. Lecture Notes in Math. 815, Springer Verlag, Berlin, Heidelberg, New York, 1980. Google Scholar

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