Representations of A-type Hecke algebras

2009/12/18 by A. P. Isaev, Isaev, A. P., O. Ogievetsky +1
Mathematics · #20C08 #81R50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0912.3701

openalex publication_date 2009/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Modular representations of Hecke algebras
• The representation dimension of Hecke algebras and symmetric groups
• On Matrix Quantum Groups of type A_n
• Representations of rank two affine Hecke algebras
• A Construction of Coxeter Group Representations (II)