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Degrees of Regular Sequences With a Symmetric Group Action

Part of: Representation theory of groups General commutative ring theory

Published online by Cambridge University Press:  07 January 2019

Federico Galetto ,
Anthony Vito Geramita  and
David Louis Wehlau
Federico Galetto
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton ON L8S 4K1 Email: galettof@math.mcmaster.ca
Anthony Vito Geramita
Affiliation:
Department of Mathematics, Queen’s University, Kingston ON K7L 3N6 Email: tony@mast.queensu.ca
David Louis Wehlau
Affiliation:
Department of Mathematics and Computer Science, Royal Military College, Kingston ON K7K 7B4 Email: wehlau@rmc.ca
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Abstract

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We consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible isomorphism types for these ideals. Following up on that work, we now analyze the possible degrees of the elements in such regular sequences. For each case of our classification, we provide some criteria guaranteeing the existence of regular sequences in certain degrees.

Keywords

complete intersectionsymmetric groupregular sequence

MSC classification

Primary: 13A02: Graded rings
Secondary: 13A50: Actions of groups on commutative rings; invariant theory 20C30: Representations of finite symmetric groups

Information

Type
Article
Information
Canadian Journal of Mathematics , Volume 71 , Issue 3 , June 2019 , pp. 557 - 578
Copyright
© Canadian Mathematical Society 2018 

Footnotes

The authors gratefully acknowledge the partial support of NSERC for this work.

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