Journal of Lie Theory Volume 6 (1996) 249–269 C ◯1996 Heldermann Verlag

On invariants of a set of matrices

E. B. Vinberg

Communicated by K. H. Hofmann

Abstract. For any connected reductive linear group H⊂SL_{n}(k) it is proved that the algebra of invariants of a set of matrices X_{1},...,X_{p}∈H (p⩾2) under simultaneous conjugations by matrices of N(H) is the normalization of the algebra generated by the traces tr X_{i1} ...X_{ik} .

Chair of Algebra Moscow University 119899 Moscow Russia vinberg@ebv.pvt.msu.su

Received October 23, 1995 and in final form October 4, 1996

ISSN 0949–5932 / $2.50 ^{_{C} ◯} Heldermann Verlag