Abstract
A monomial basis for Z(ZSn), the centre of the symmetric group algebra, or Z(Hn), the centre of the corresponding Iwahori-Hecke algebra, is a basis that consists solely of monomial symmetric polynomials in Jucys- Murphy elements. In a previous paper, we showed that there are only finitely many monomial bases for Z(ZS3) and Z(H3). In this paper, we prove that there exist infinitely many monomial bases for Z(ZS4), which we characterize completely. Using this result, we are able to produce three new integral bases for Z(H4), each of which is monomial. Based on extensive computer calculations, we conjecture that our list of monomial bases for Z(H4) is exhaustive. In addition, we provide evidence to support the conjectures that the number of monomial bases for Z(ZS5) is finite, and that no monomial bases exist for Z(H5).
| Original language | English |
|---|---|
| Pages (from-to) | 119-143 |
| Number of pages | 25 |
| Journal | Far East Journal of Mathematical Sciences |
| Volume | 58 |
| Issue number | 2 |
| Publication status | Published - 2011 |
Keywords
- algebra
- centre
- monomial basis
- symmetric group
- symmetric polynomial