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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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Proof of a conjecture of Kostant
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by Dragomir Ž. Đoković PDF
Trans. Amer. Math. Soc. 302 (1987), 577-585 Request permission

Abstract:

Let ${\mathfrak {g}_0} = {\mathfrak {k}_0} + {\mathfrak {p}_0}$ be a Cartan decomposition of a semisimple real Lie algebra and $\mathfrak {g} = \mathfrak {k} + \mathfrak {p}$ its complexification. Denote by $G$ the adjoint group of $\mathfrak {g}$ and by ${G_0},K,{K_0}$ the connected subgroups of $G$ with respective Lie algebras ${\mathfrak {g}_0},\mathfrak {k},{\mathfrak {k}_0}$. A conjecture of Kostant asserts that there is a bijection between the ${G_0}$-conjugacy classes of nilpotent elements in ${\mathfrak {g}_0}$ and the $K$-orbits of nilpotent elements in $\mathfrak {p}$ which is given explicitly by the so-called Cayley transformation. This conjecture is proved in the paper.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 302 (1987), 577-585
  • MSC: Primary 17B20; Secondary 17B45, 22E60
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0891636-0
  • MathSciNet review: 891636