Braids, Shuffles and Symmetrizers

Abstract

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.

18 pages

References in corpus (4)

• The Algebra and Combinatorics of Shuffles and Multiple Zeta Values
• Quantum group covariant (anti)symmetrizers, epsilon-tensors, vielbein, Hodge map and Laplacian
• Orthogonal and Symplectic Quantum Matrix Algebras and Cayley-Hamilton Theorem for them
• Braidings of Tensor Spaces

Cited by in corpus (5)

• Josephson effect in Graphene SNS Junction with a Single Localized Defect
• Baxterisation of the fused Hecke algebra and R-matrices with gl(N)-symmetry
• Braidings of Tensor Spaces
• Cyclotomic shuffles
• A quantum shuffle approach to quantum determinants