On the mutually commuting n-tuples in compact groups

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups

probability of mutually commuting n-tuples in some classes of compact groups

Cohomology of the Space of Commuting N-tuples in a Compact Lie Group

Consider the space Hom(Z n , G) of pairwise commuting n-tuples of elements in a compact Lie group G. This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingulariza-tion of the generic component of Hom(Z n , G), which allows us to derive formulas for its singular and equivariant cohomology in terms of the Lie algebra of a maximal torus in G and the ...

Almost commuting elements in compact Lie groups

Unitary N-dilations for Tuples of Commuting Matrices

We show that whenever a contractive k-tuple T on a finite dimensional space H has a unitary dilation, then for any fixed degree N there is a unitary k-tuple U on a finite dimensional space so that q(T ) = PHq(U)|H for all polynomials q of degree at most N .