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• W1736861856 abstract "In 1936, Margarete C. Wolf showed that the ring of symmetric free polynomials in two or more variables is isomorphic to the ring of free polynomials in infinitely many variables. We show that Wolf's theorem is a special case of a general theory of the ring of invariant free polynomials: every ring of invariant free polynomials is isomorphic to a free polynomial ring. Furthermore, we show that this isomorphism extends to the free functional calculus as a norm-preserving isomorphism of function spaces on a domain known as the row ball. We give explicit constructions of the ring of invariant free polynomials in terms of representation theory and develop a rudimentary theory of their structures. Specifically, we obtain a generating function for the number of basis elements of a given degree and explicit formulas for good bases in the abelian case." @default.
• W1736861856 created "2016-06-24" @default.
• W1736861856 creator A5005813786 @default.
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• W1736861856 date "2014-09-05" @default.
• W1736861856 modified "2023-09-27" @default.
• W1736861856 title "Free functions with symmetry" @default.
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• W1736861856 hasPublicationYear "2014" @default.
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