Standard symmetrizing forms and Murphy bases of the cyclotomic Hecke algebras

2025/12/11 by Hu, Jun, Li, Huansheng
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2512.10202

Abstract

In this paper we compute the explicit value of the standard symmetrizing form of the cyclotomic Hecke algebra of type G(ℓ,1,n) on each Murphy basis element. We do this for both the non-degenerate cyclotomic Hecke algebra of type G(ℓ,1,n) and the degenerate cyclotomic Hecke algebra of type G(ℓ,1,n). As an application, we obtain some equations on the coefficients which occur in the transition matrix between the Murphy basis elements and the seminormal basis elements of the cyclotomic Hecke algebra of type G(ℓ,1,n).

Citations

• On the cocenter of the cyclotomic Hecke algebra of type G(r,1,n)
• Trace forms on the cyclotomic Hecke algebras and cocenters of the cyclotomic Schur algebras
• Matrix units and Schur elements for the degenerate cyclotomic Hecke algebras
• Graded induction for Specht modules
• Cyclotomic Nazarov-Wenzl algebras
• Matrix units and generic degrees for the Ariki--Koike algebras

Related

• On the seminormal bases and dual seminormal bases of the cyclotomic Hecke algebras of type G(ℓ,1,n)
• Matrix units and Schur elements for the degenerate cyclotomic Hecke algebras
• The idempotents in cyclotomic Hecke algebras and periodic property of the Jucys-Murphy elements
• Seminormal basis for the cyclotomic Hecke algebra of type G(r,p,n)
• Jucys--Murphy elements and representations of cyclotomic Hecke algebras