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Defect in cyclotomic Hecke algebras
- Publication Year :
- 2021
-
Abstract
- The complexity of a block of a symmetric algebra can be measured by the notion of defect, a numerical datum associated to each of the simple modules contained in the block. Geck showed that the defect is a block invariant for Iwahori-Hecke algebras of finite Coxeter groups in the equal parameter case, and speculated that a similar result should hold in the unequal parameter case. We conjecture that the defect is a block invariant for all cyclotomic Hecke algebras associated with complex reflection groups, and we prove it for the groups of type $G(l,p,n)$ and for the exceptional types for which the blocks are known. In particular, for the groups $G(l,1,n)$, we show that the defect corresponds to the notion of weight in the sense of Fayers, for which we thus obtain a new way of computation. We also prove that the defect is a block invariant for cyclotomic Yokonuma-Hecke algebras.<br />Comment: 25 pages
- Subjects :
- Mathematics - Representation Theory
20C08, 05E10, 20C20
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2105.08580
- Document Type :
- Working Paper