Loops in SU(2) and factorization

We discuss analytic issues associated with a refinement of triangular factorization for the loop group of SU(2). This factorization is of interest because (1) Toeplitz determinants factor in the associated coordinates, and (2) the factorization is intimately related to the critical degree of smoothness for loops, W1/2,L2 . © 2011 Elsevier Inc. All rights reserved.