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On Some Quadratic Algebras: Jucys—Murphy and Dunkl Elements

  • Anatol N. Kirillov
Part of the CRM Series in Mathematical Physics book series (CRM)

Abstract

We study some quadratic algebras that appeared in low- dimensional topology and Schubert calculus. We introduce Jucys—Murphy elements in the braid algebra and in the pure braid group, as well as Dunkl elements in the extended affine braid group. Relationships between the Dunkl elements, Dunkl operators and Jucys-Murphy elements are described.

Keywords

Symmetric Group Braid Group Coxeter Group Hilbert Series Quadratic Algebra 
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© Springer Science+Business Media New York 2000

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  • Anatol N. Kirillov

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