Braids, Shuffles and Symmetrizers

Details Braids, Shuffles and Symmetrizers Braids, Shuffles and Symmetrizers

2008-12-20

arxiv.org/abs/0812.3974v1

J. Phys. A: Math. Theor. 42 (2009) 304017

Mathematics

Quantum Algebra

18 pages

Scientific paper

10.1088/1751-8113/42/30/304017

Multiplicative analogues of the shuffle elements of the braid group rings are introduced; in local representations they give rise to certain graded associative algebras (b-shuffle algebras). For the Hecke and BMW algebras, the (anti)-symmetrizers have simple expressions in terms of the multiplicative shuffles. The (anti)-symmetrizers can be expressed in terms of the highest multiplicative 1-shuffles (for the Hecke and BMW algebras) and in terms of the highest additive 1-shuffles (for the Hecke algebras). The spectra and multiplicities of eigenvalues of the operators of the multiplication by the multiplicative and additive 1-shuffles are examined.

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