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An Explicit Cell Decomposition of the Wonderful Compactification of a Semisimple Algebraic Group

Published online by Cambridge University Press:  20 November 2018

Lex E. Renner
Lex E. Renner*
Affiliation:
Department of Mathematics, The University of Western Ontario, London, Ontario, N6A 5B7
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Abstract

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We determine an explicit cell decomposition of the wonderful compactification of a semisimple algebraic group. To do this we first identify the $B\,\times \,B$-orbits using the generalized Bruhat decomposition of a reductive monoid. From there we show how each cell is made up from $B\,\times \,B$-orbits.

Keywords

14L3014M1720M17
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 1 , 01 March 2003 , pp. 140 - 148
Copyright
Copyright © Canadian Mathematical Society 2003

References

[1] Bialynicki-Birula, A., Some theorems on actions of algebraic groups. Ann. of Math. 98 (1973), 480–497.Google Scholar
[2] Brion, M., The behaviour at infinity of the Bruhat decomposition. Comment.Math. Helv. 73 (1998), 137–174.Google Scholar
[3] Carter, R., Finite groups of Lie type, conjugacy classes and complex characters. John Wiley and Sons, New York, 1985.Google Scholar
[4] DeConcini, C. and Procesi, C., Complete symmetric varieties. Lecture Notes in Math. 996, Springer, 1973, 1–44.Google Scholar
[5] DeConcini, C. and Springer, T. A., Compactification of symmetric varieties. J. Transform. Groups 4 (1999), 273–300.Google Scholar
[6] Pennell, E. A., Putcha, M. S. and Renner, L. E., Analogue of the Bruhat-Chevalley order for reductive monoids. J. Algebra 196 (1997), 339–368.Google Scholar
[7] Putcha, M. S., Linear algebraic monoids. Cambridge University Press, Cambridge, UK, 1988.Google Scholar
[8] Putcha, M. S. and Renner, L. E., The system of idempotents and the lattice of J-classes of reductive algebraic monoids. J. Algebra 116 (1988), 385–399.Google Scholar
[9] Renner, L. E., Analogue of the Bruhat decomposition for algebraic monoids. J. Algebra 101 (1986), 303–338.Google Scholar
[10] Renner, L. E., Classification of semisimple algebraic monoids. Trans. Amer. Math. Soc. 292 (1985), 193–223.Google Scholar
[11] Renner, L. E., Classification of semisimple varieties. J. Algebra 122 (1989), 275–287.Google Scholar
[12] Richardson, R. W. and Springer, T. A., The Bruhat order on symmetric varieties. Geom. Dedicata 35 (1990), 389–436.Google Scholar
[13] Strickland, E., A vanishing theorem for group compactifications. Math. Ann. 277 (1987), 165–171.Google Scholar