5. References (2)

• Centralizer algebra for tensor product decompositions of classical groups • Quantum version (BMW, Kauffman) plays the same role for quantum groups • Rewriting monomials in Brauer algebra helps to control the quantum version department of mathematics and computer scienceJJ J N I II 4/65 Symmetric group by diagrams y y y y y y y y Figure 1: A diagram for (2, 4, 3) Permutations represented by diagrams Multiplication by composition department of mathematics and computer scienceJJ J N I II 5/65 Extension to Brauer monoid z z z z zz zz Figure 2: A Brauer diagram Diagramwise: add horizontal strands Closed loop (after compositions): δ (δ is a coefficient) department of mathematics and computer scienceJJ J N I II 6/65 Dimension of the Brauer algebra overQ(δ