Abstract
In this note, we find a monomial basis of the cyclotomic Hecke algebra \({\mathcal{H}_{r,p,n}}\) of G(r,p,n) and show that the Ariki-Koike algebra \({\mathcal{H}_{r,n}}\) is a free module over \({\mathcal{H}_{r,p,n}}\), using the Gröbner-Shirshov basis theory. For each irreducible representation of \({\mathcal{H}_{r,p,n}}\), we give a polynomial basis consisting of linear combinations of the monomials corresponding to cozy tableaux of a given shape.
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This research was supported by KRF Grant # 2005-070-C00004 and a research grant from Seoul Women’s University (2009).
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Lee, Di. Cyclotomic Hecke Algebras of G(r, p, n). Algebr Represent Theor 13, 705–718 (2010). https://doi.org/10.1007/s10468-009-9170-5
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DOI: https://doi.org/10.1007/s10468-009-9170-5
Keywords
- Complex reflection group
- Cyclotomic Hecke algebra
- Gröbner-Shirshov basis
- Representation
- Specht module
- Cozy tableau