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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Unipotent characters of the even orthogonal groups over a finite field
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by George Lusztig PDF
Trans. Amer. Math. Soc. 272 (1982), 733-751 Request permission

Abstract:

The characters of unipotent representations of a simple algebraic group over $F_q$ of type $\ne D_n$ on any regular semisimple element are explicitly known for large $q$. This paper deals with the remaining case: type $D_n$.
References
  • Teruaki Asai, On the zeta functions of the varieties $X(w)$ of the split classical groups and the unitary groups, Osaka J. Math. 20 (1983), no. 1, 21–32. MR 695614
  • G. Lusztig, Irreducible representations of finite classical groups, Invent. Math. 43 (1977), no. 2, 125–175. MR 463275, DOI 10.1007/BF01390002
  • George Lusztig, Representations of finite Chevalley groups, CBMS Regional Conference Series in Mathematics, vol. 39, American Mathematical Society, Providence, R.I., 1978. Expository lectures from the CBMS Regional Conference held at Madison, Wis., August 8–12, 1977. MR 518617
  • George Lusztig, Unipotent characters of the symplectic and odd orthogonal groups over a finite field, Invent. Math. 64 (1981), no. 2, 263–296. MR 629472, DOI 10.1007/BF01389170
  • —, A class of irreducible representations of a Weyl group. II, Proc. Kon. Nederl. Akad. A85 (1982),
  • George Lusztig, Characters of reductive groups over a finite field, Annals of Mathematics Studies, vol. 107, Princeton University Press, Princeton, NJ, 1984. MR 742472, DOI 10.1515/9781400881772
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 272 (1982), 733-751
  • MSC: Primary 20G05; Secondary 20C15
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0662064-3
  • MathSciNet review: 662064