Geodesic
Conjugacy Classes and Nilpotent Variety of a Reductive Monoid
Canadian journal of mathematics, Tome 50 (1998) no. 4, pp. 829-843

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

We continue in this paper our study of conjugacy classes of a reductive monoid $M$ . The main theorems establish a strong connection with the Bruhat-Renner decomposition of $M$ . We use our results to decompose the variety ${{M}_{\text{nil}}}$ of nilpotent elements of $M$ into irreducible components. We also identify a class of nilpotent elements that we call standard and prove that the number of conjugacy classes of standard nilpotent elements is always finite.
DOI : 10.4153/CJM-1998-044-7
Mots-clés : 20G99, 20M10, 14M99, 20F55 
Conjugacy Classes and Nilpotent Variety of a Reductive Monoid. Canadian journal of mathematics, Tome 50 (1998) no. 4, pp. 829-843. doi: 10.4153/CJM-1998-044-7
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[1] 1. Carter, R. W., Finite groups of Lie type: Conjugacy classes and complex characters. Wiley, 1985. Google Scholar

[2] 2. Humphreys, J. E., Reflection groups and Coxeter groups. Cambridge Univ. Press, 1990. Google Scholar

[3] 3. Lusztig, G., On the finiteness of the number ofunipotent classes. Invent. Math. 34(1976), 201-213. Google Scholar

[4] 4. Pennell, E. A., Putcha, M. S. and Renner, L. E., Analogue of the Bruhat-Chevally order for reductive monoids. J. Algebr. 196(1997), 339-368. Google Scholar

[5] 5. Putcha, M. S., Regular linear algebraic monoids. Trans. Amer. Math. Soc. 290(1985), 615-626. Google Scholar

[6] 6. Putcha, M. S., Linear algebraic monoids. London Math. Soc., Lecture Note Series 133, Cambridge Univ. Press, 1988. Google Scholar

[7] 7. Putcha, M. S., Conjugacy classes in algebraic monoids. Trans. Amer. Math. Soc. 303(1987), 529—540. Google Scholar

[8] 8. Putcha, M. S., Conjugacy classes in algebraic monoids II. Canad. J. Math. 46(1994), 648-661. Google Scholar

[9] 9. Putcha, M. S. and Renner, L. E., The system ofidempotents and the lattice of J-classes of reductive algebraic monoids. J. Algebr. 116(1988), 385-399. Google Scholar

[10] 10. The canonical compactification of a finite group of Lie type. Trans. Amer. Math. Soc. 337(1993), 305-319. Google Scholar

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