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Degrees of regular sequences with a symmetric group action

  • Federico Galetto,
    Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1
  • Anthony Vito Geramita,
    Department of Mathematics, Queen's University, Kingston, ON K7L 3N6
  • David Louis Wehlau,
    Department of Mathematics and Computer Science, Royal Military College, Kingston, ON K7K 7B4
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Abstract

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 intersection, symmetric group, regular sequences Complete intersection, symmetric group, regular sequences
MSC Classifications: 13A02, 13A50, 20C30 show english descriptions Graded rings [See also 16W50]
Actions of groups on commutative rings; invariant theory [See also 14L24]
Representations of finite symmetric groups
13A02 - Graded rings [See also 16W50]
13A50 - Actions of groups on commutative rings; invariant theory [See also 14L24]
20C30 - Representations of finite symmetric groups
 

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