Finite SAGBI bases for polynomial invariants of conjugates of alternating groups

  • Authors:

  • Manfred Göbel

  • Affiliations:

  • -

  • Venue:
  • Mathematics of Computation
  • Year:
  • 2002

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Abstract

It is well-known, that the ring C[X1,..., Xn]An of polynomial invariants of the alternating group An has no finite SAGBI basis with respect to the lexicographical order for any number of variables n ≥ 3. This note proves the existence of a nonsingular matrix δn ∈ GL(n, C) such that the ring of polynomial invariants C[X1,..., Xn]Anδn, where Anδn denotes the conjugate of An with respect to δn, has a finite SAGBI basis for any n ≥ 3.