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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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On automorphisms of matrix invariants
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by Zinovy Reichstein PDF
Trans. Amer. Math. Soc. 340 (1993), 353-371 Request permission

Abstract:

Let ${Q_{m,n}}$ be the space of $m$-tuples of $n \times n$-matrices modulo the simultaneous conjugation action of $PG{L_n}$. Let ${Q_{m,n}}(\tau )$ be the set of points of ${Q_{m,n}}$ of representation type $\tau$. We show that for $m \geq n + 1$ the group $\operatorname {Aut}({Q_{m,n}})$ of representation type preserving algebraic automorphisms of ${Q_{m,n}}$ acts transitively on each ${Q_{m,n}}(\tau )$. Moreover, the action of $\operatorname {Aut}({Q_{m,n}})$ on the Zariski open subset ${Q_{m,n}}(1,n)$ of ${Q_{m,n}}$ is $s$-transitive for every positive integer $s$. We also prove slightly weaker analogues of these results for all $m \geq 3$.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 340 (1993), 353-371
  • MSC: Primary 16R30
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1124173-1
  • MathSciNet review: 1124173