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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Singularities in the nilpotent scheme of a classical group
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by Wim Hesselink PDF
Trans. Amer. Math. Soc. 222 (1976), 1-32 Request permission


If $(X,x)$ is a pointed scheme over a ring k, we introduce a (generalized) partition ${\text {ord}}(x,X/k)$. If G is a reductive group scheme over k, the existence of a nilpotent subscheme $N(G)$ of ${\text {Lie}}(G)$ is discussed. We prove that ${\text {ord}}(x,N(G)/k)$ characterizes the orbits in $N(G)$, their codimension and their adjacency structure, provided that G is $G{l_n}$, or $S{p_n}$ and $1/2 \in k$. For $S{O_n}$ only partial results are obtained. We give presentations of some singularities of $N(G)$. Tables for its orbit structure are added.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 222 (1976), 1-32
  • MSC: Primary 14B05; Secondary 14L15
  • DOI:
  • MathSciNet review: 0429875