Journal article
Free functions with symmetry
Mathematische Zeitschrift, v 289(3-4), pp 837-857
01 Aug 2018
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.
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Details
- Title
- Free functions with symmetry
- Creators
- David Cushing - Durham UniversityJ. E. Pascoe - Washington University in St. LouisRyan Tully-Doyle - University of New Haven
- Publication Details
- Mathematische Zeitschrift, v 289(3-4), pp 837-857
- Publisher
- Springer Berlin Heidelberg
- Grant note
- University of Durham
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000439449900004
- Scopus ID
- 2-s2.0-85032971553
- Other Identifier
- 991021879784104721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics