Z. Reichstein, N. Vonessen, Group actions and invariants in algebras of generic matrices, Advances in Applied Mathematics 37, issue 4, October 2006, 481--500.

Abstract: We show that the fixed elements for the natural GLm-action on the universal division algebra UD(m, n) of m generic n x n-matrices form a division subalgebra of degree n, assuming n >= 3 and 2 <= m <= n^2 -2. This allows us to give an asymptotic estimate on the dimension of the space of SLm-invariant homogeneous central polynomials p(X_1, ..., X_m) for n x n-matrices. Here the base field is assumed to be of characteristic zero.

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