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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some intersection properties of the fibres of Springer’s resolution
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by James S. Wolper PDF
Proc. Amer. Math. Soc. 91 (1984), 182-188 Request permission

Abstract:

Combinatorial results are used to calculate the dimension of the intersection of any two irreducible components of the set in the flag variety fixed by the action of a unipotent element of ${\text {G}}{{\text {L}}_n}$ whose Jordan decomposition has two blocks. This is then related to the "left cells" of Kazhdan and Lusztig, which are used to construct representations of ${S_n}$, the Weyl group of ${\text {G}}{{\text {L}}_n}$.
References
  • David Kazhdan and George Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), no. 2, 165–184. MR 560412, DOI 10.1007/BF01390031
  • D. E. Knuth, The art of computer programming, Vol. III, Addison-Wesley, Reading, Mass., 1973. Alain Lascoux and M-P. Schützenberger, Polynômes de Kazhdan and Lusztig pour les Grassmanniennes, Astérisque, Soc. Math. France, Paris, 87-88.
  • N. Spaltenstein, The fixed point set of a unipotent transformation on the flag manifold, Nederl. Akad. Wetensch. Proc. Ser. A 79=Indag. Math. 38 (1976), no. 5, 452–456. MR 0485901
  • Robert Steinberg, Conjugacy classes in algebraic groups, Lecture Notes in Mathematics, Vol. 366, Springer-Verlag, Berlin-New York, 1974. Notes by Vinay V. Deodhar. MR 0352279
  • J. A. Vargas, Fixed points under the action of unipotent elements of $\textrm {SL}_{n}$ in the flag variety, Bol. Soc. Mat. Mexicana (2) 24 (1979), no. 1, 1–14. MR 579665
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 91 (1984), 182-188
  • MSC: Primary 20G99; Secondary 14L30
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0740166-8
  • MathSciNet review: 740166