On some quadratic algebras
Abstract
Description
We study some quadratic algebras which are appeared in the low-dimensional topology and Schubert calculus. We introduce the Jucys-Murphy elements in the braid algebra and in the pure braid group, as well as the Dunkl elements in the extended affine braid group. Relationships between the Dunkl elements, Dunkl operators and Jucys-Murphy elements are described.
LaTeX, 28 pages. In revised version a new Section and new remarks are added. Some typos are corrected
LaTeX, 28 pages. In revised version a new Section and new remarks are added. Some typos are corrected