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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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Functional equations for character series associated with $n\times n$ matrices
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by Edward Formanek PDF
Trans. Amer. Math. Soc. 294 (1986), 647-663 Request permission

Abstract:

Let $A$ be either the ring of invariants or the trace ring of $r$ generic $n \times n$ matrices. Then $A$ has a character series $\chi (A)$ which is a symmetric rational function of commuting variables ${x_1}, \ldots ,{x_r}$. The main result is that if $r \geq {n^2}$, then $\chi (A)$ satisfies the functional equation \[ \chi (A)(x_1^{ - 1}, \ldots ,x_r^{ - 1}) = {( - 1)^d}{({x_1} \cdots {x_r})^{{n^2}}}\chi (A)({x_1}, \ldots ,{x_r})\], where $d$ is the Krull dimension of $A$.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 647-663
  • MSC: Primary 15A72; Secondary 16A38
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0825728-8
  • MathSciNet review: 825728