The Calogero-Moser partition for G(m,d,n)
Gwyn Bellamy
TL;DR
This paper demonstrates how to derive the Calogero-Moser partition for complex reflection groups G(m,d,n) from the known partition of G(m,1,n), confirming a conjecture relating it to Rouquier families.
Contribution
It provides a method to deduce the Calogero-Moser partition for G(m,d,n) from G(m,1,n), confirming a conjecture connecting it to Rouquier families.
Findings
Calogero-Moser partition for G(m,d,n) can be derived from G(m,1,n)
Confirms Gordon and Martino's conjecture for W = G(m,d,n)
Links Calogero-Moser partition to Rouquier families in cyclotomic Hecke algebras
Abstract
We show that it is possible to deduce the Calogero-Moser partition of the irreducible representations of the complex reflection groups G(m,d,n) from the corresponding partition for G(m,1,n). This confirms, in the case W = G(m,d,n), a conjecture of Gordon and Martino relating the Calogero-Moser partition to Rouquier families for the corresponding cyclotomic Hecke algebra.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Molecular spectroscopy and chirality