On some quadratic algebras

Details On some quadratic algebras On some quadratic algebras

1997-05-06

arxiv.org/abs/q-alg/9705003v3

Mathematics

Quantum Algebra

LaTeX, 28 pages. In revised version a new Section and new remarks are added. Some typos are corrected

Scientific paper

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.

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