Group actions and invariants in algebras of generic matrices

Z. Reichstein, N. Vonessen

Research output: Contribution to journalArticlepeer-review

Abstract

We show that the fixed elements for the natural GLm-action on the universal division algebra UD (m, n) of m generic n × n-matrices form a division subalgebra of degree n, assuming n ≥ 3 and 2 ≤ m ≤ n2 - 2. This allows us to describe the asymptotic behavior of the dimension of the space of SLm-invariant homogeneous central polynomials p (X1, ..., Xm) for n × n-matrices. Here the base field is assumed to be of characteristic zero.

Original languageEnglish
Pages (from-to)481-500
Number of pages20
JournalAdvances in Applied Mathematics
Volume37
Issue number4
DOIs
StatePublished - Oct 2006

Keywords

  • Central polynomial
  • Concomitants
  • Gelfand-Kirillov dimension
  • Generic matrices
  • Geometric action
  • Group action
  • Invariants
  • PI-degree
  • Universal division algebra

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