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The flag major index on conjugacy classes of wreath products
Abstract
A classical result, independently proved by Garsia and by Wachs, gives a simple and elegant closed expression for the evaluation, at a primitive root of unity, of the major index generating function over a conjugacy class in the symmetric group. In this paper, we generalize this result to the flag major index generating function over conjugacy classes in any wreath product ℤrwr Sn. Our approach is new, and applies conjugation by a Coxeter element as a cyclic group action on the conjugacy class. This leads to a simple formula in the general case.
Related
- Sn-equivariant L-classes of Cartesian powers of Witt spaces and the Hodge index conjecture for symmetric products
- On the number of ℓ-regular conjugacy classes
- Categorical and Floer-theoretic entropies: comparison and counting conjugacy classes in symplectic mapping class groups
- Homological finiteness properties of wreath products
- Representation zeta functions of wreath products with finite groups
BibTeX
@misc{rozenfeld2026flag,
title = {{The flag major index on conjugacy classes of wreath products}},
author = {Harel Rozenfeld},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34970},
eprint = {2610.34970},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34970},
}
RIS
TY - UNPB
TI - The flag major index on conjugacy classes of wreath products
AU - Harel Rozenfeld
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34970
UR - https://arxiv.org/abs/2610.34970
AB - A classical result, independently proved by Garsia and by Wachs, gives a simple and elegant closed expression for the evaluation, at a primitive root of unity, of the major index generating function over a conjugacy class in the symmetric group. In this paper, we generalize this result to the flag major index generating function over conjugacy classes in any wreath product ℤ_rwr S_n. Our approach is new, and applies conjugation by a Coxeter element as a cyclic group action on the conjugacy class. This leads to a simple formula in the general case.
ER -