Matrix units and Schur elements for the degenerate cyclotomic Hecke algebras

2011/10/08 by Deke Zhao, Zhao, Deke · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.RA #math.RT #msc:16G99 #msc:20C20 #msc:20G05

paper · pdf · doi:10.48550/arxiv.1110.1735

Comments most welcome! arXiv admin note: substantial text overlap with arXiv:math/0108164 by a different author

arxiv created 2011/10/08 · arxiv updated 2011/10/11

Abstract

The paper uses the cellular basis of the (semi-simple) degenerate cyclotomic Hecke algebras to investigate these algebras exhaustively. As a consequence, we describe explicitly the "Young's seminormal form" and a orthogonal bases for Specht modules and determine explicitly the closed formula for the natural bilinear form on Specht modules and Schur elements for the degenerate cyclotomic Hekce algebras.

Citations

• Matrix units and generic degrees for the Ariki--Koike algebras

Cited by

• Standard symmetrizing forms and Murphy bases of the cyclotomic Hecke algebras

Related

• Trace forms on the cyclotomic Hecke algebras and cocenters of the cyclotomic Schur algebras
• Fusion procedure for Degenerate cyclotomic Hecke algebras
• Restricting Specht modules of cyclotomic Hecke algebras
• Standard symmetrizing forms and Murphy bases of the cyclotomic Hecke algebras
• An isomorphism theorem for degenerate cyclotomic Yokonuma-Hecke algebras and applications