Finite SAGBI bases for polynomial invariants of conjugates of alternating groups

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 n GL(n, C) such that the ring of polynomial invariants C[X1, . . . , Xn]An n , where An n denotes the conjugate of An with respect to n, has a finite SAGBI basis for any n 3.

• Type: Journal
• Year: 2002
• Where: MOC
• Authors: Manfred Göbel
• Keywords: Alternating Group, Finite Sagbi Basis, MOC 2002, Polynomial Invariants