2007/05/11 by Andrew Francis, Lenny Jones, Francis, Andrew +1 · 1 citation
Mathematics · #16S34 #20B30 #20C05 #20C08 (primary) #20C30 (secondary)} #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.0705.1581
openalex publication_date 2007/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a recursive algorithm that produces an integral basis for the centre of the Hecke algebra of type A consisting of linear combinations of monomial symmetric polynomials of Jucys--Murphy elements. We also discuss the existence of integral bases for the centre of the Hecke algebra that consist solely of monomial symmetric polynomials of Jucys--Murphy elements. Finally, for n=3, we show that only one such basis exists for the centre of the Hecke algebra, by proving that there are exactly four bases for the centre of the corresponding symmetric group algebra which consist solely of monomial symmetric polynomials of Jucys--Murphy elements.