Symmetrizers and antisymmetrizers for the BMW algebra

Details Symmetrizers and antisymmetrizers for the BMW algebra Symmetrizers and antisymmetrizers for the BMW algebra

2011-09-02

arxiv.org/abs/1109.0342v1

Mathematics

Quantum Algebra

Scientific paper

Let $n\in\mathds{N}$ and $B_n(r,q)$ be the generic Birman-Murakami-Wenzl algebra with respect to indeterminants $r$ and $q$. It is known that $B_n(r,q)$ has two distinct linear representations generated by two central elements of $B_n(r,q)$ called the symmetrizer and antisymmetrizer of $B_n(r,q)$. These generate for $n\geq 3$ the only one dimensional one sided ideals of $B_n(r,q)$ and generalize the corresponding notion for Hecke algebras of type $A$. In this paper the coefficients of these elements with respect to the graphical basis of $B_n(r,q)$ are determined explicitly.

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