Skein construction of idempotents in Birman-Murakami-Wenzl algebras

Details Skein construction of idempotents in Birman-Murakami-Wenzl algebras Skein construction of idempotents in Birman-Murakami-Wenzl algebras

2000-06-20

arxiv.org/abs/math/0006143v2

Mathematics

Quantum Algebra

26 pages, LaTeX with figures; Section 8 and details to the proof of Theorem 3.1 are added

Scientific paper

We give skein theoretic formulas for minimal idempotents in the Birman-Murakami-Wenzl algebras. These formulas are then applied to derive various known results needed in the construction of quantum invariants and modular categories. In particular, an elementary proof of the Wenzl formula for quantum dimensions is given. This proof does not use the representation theory of quantum groups and the character formulas.

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