Helmer Aslaksen

Defining relations of invariants of two 3×3 matrices

Over a field of characteristic 0, Teranishi, 1986, found a minimal system of eleven generators of the algebra of invariants of two 3 × 3 matrices under simultaneous conjugation by GL3. Nakamoto, 2002, obtained the explicit, but very complicated defining relation for a similar system of generators over Z. In this paper we give another natural set of eleven generators of the algebra of invariants over a field of characteristic 0 and the defining relation with respect to this generating set. Our defining relation is much simpler than that of Nakamoto.

Invariants of S 4 and the Shape of Sets of Vectors

We study a representation ofSn that is related to the shape of sets of vectors in ℝn. We want to determine the invariants of this representation, and obtain a complete description for the case ofS4.

Restricted homogeneous coordinates for the Cayley projective plane

I. Porteous has shown that the Cayley projective plane can be coordinatized in a way resembling homogeneous coordinates. We will show how to construct line coordinates in a similar way. As an illustration, we give an explicit example to show that the Cayley projective plane is not Desarguean.

Determining summands in tensor products of Lie algebra representations

Abstract We give some results that enable us to find certain summands in tensor products of Lie algebra representations. We concentrate on the splitting of tensor squares into their symmetric and antisymmetric parts. Our results are valid for any Lie algebra of arbitrary rank, but we do not attempt to give the complete decomposition.

Invariant Theory of Matrices

Let F be a field of characteristic 0, let M(n, m) =M(n, m, F) denote the set of n x m matrices over F and let W = W (n, m, F) be the vector space of m-tuples of n x n matrices over F. Let V ⊂ W be a vector space on which a group G ⊂ GL(n, F) acts by simultaneous conjugation. We will denote the polynomial functions on V by P(V) and the G invariants by P(V) G .

K-Theory for the Integer Heisenberg Groups

We give a closed formula for topological K-theory of the homogeneous space N=0 , where 0 is the standard integer lattice in the simply connected Heisenberg Lie group N of dimension 2nC 1, n2 Z C. The main tools in our calculations are obtained by computing diagonal forms for

On O m × G L n Highest Weight Vectors

Let ℂm,n be the vector space of m×n complex matrices and P(ℂm,n) be the algebra of complex-valued polynomials on ℂm,n. Let GL m ×GL n act on P(ℂm,n) by pre-and post-multiplication as follows:

Generic 2×2 matrices with involution

\left( {{g_1},{g_2}} \right)f\left( x \right) = f\left( {g_1^{ - 1}x{g_2}} \right)