Mathematics – Quantum Algebra
Scientific paper
2009-12-18
Mathematics
Quantum Algebra
11 pages, Proceedings of International Workshop "Supersymmetries and Quantum Symmetries", Dubna, 2006
Scientific paper
We review some facts about the representation theory of the Hecke algebra. We adapt for the Hecke algebra case the approach of Okounkov and Vershik which was developed for the representation theory of symmetric groups. We justify an explicit construction of the idempotents in the Hecke algebra in terms of Jucys-Murphy elements. Ocneanu's traces for these idempotents (which can be interpreted as q-dimensions of corresponding irreducible representations of quantum linear groups) are presented.
Isaev A. P.
Ogievetsky Oleg
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