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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 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Functional equations for character series associated with $n\times n$ matrices
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by Edward Formanek
Trans. Amer. Math. Soc. 294 (1986), 647-663
DOI: https://doi.org/10.1090/S0002-9947-1986-0825728-8

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 $A$.
References
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Bibliographic 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