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Eirini Chavli

Publications and source records attributed to Eirini Chavli.

12 recordsLinked to original sources
arXiv2026

Interval Garside groups arising from involutions in finite reflection groups

We identify and study the interval Garside groups arising from the restriction of the absolute order on a Coxeter group to a lattice $[1,w]_T$, where $w$ is an involution. Those involutions $w$ for which $[1,w]_T$ is a lattice were previously classified by the second author; every such involution lies in the center of the parabolic subgroup generated by $[1,w]_T$. Except in type $B_n$, the obtained groups are isomorphic to (decomposable) right-angled Artin groups. We also investigate the situation for some finite complex reflection groups, mostly in rank two, taking for $w$ a (not necessarily involutive) central element.

math.GR↗
arXiv2025

Homological algebra of Nakayama algebras and 321-avoiding permutations

Linear Nakayama algebras over a field $K$ are in natural bijection to Dyck paths and Dyck paths are in natural bijection to 321-avoiding bijections via the Billey-Jockusch-Stanley bijection. Thus to every 321-avoiding permutation $π$ we can associate in a natural way a linear Nakayama algebra $A_π$. We give a homological interpretation of the fixed points statistic of 321-avoiding permutations using Nakayama algebras with a linear quiver. We furthermore show that the space of self-extension for the Jacobson radical of a linear Nakayama algebra $A_π$ is isomorphic to $K^{\mathfrak{s}(π)}$, where $\mathfrak{s}(π)$ is defined as the cardinality $k$ such that $π$ is the minimal product of transpositions of the form $s_i=(i,i+1)$ and $k$ is the number of distinct $s_i$ that appear.

math.CO↗
arXiv2025

The BMM Symmetrising Trace Conjecture for Families of Complex Reflection Groups of Rank Two

The exceptional complex reflection groups of rank 2 are partitioned into three families. We construct explicit matrix models for the Hecke algebras associated to the maximal groups in the tetrahedral and octahedral family, and use them to verify the BMM symmetrising trace conjecture for all groups in these two families, providing evidence that a similar strategy might apply for the icosahedral family.

math.RT↗
arXiv2024

The center of the walled Brauer algebra $B_{r,1}(δ)$

We show that the centre of the walled Brauer algebra $B_{r,1}(δ)$ over the complex field $\mathbb{C}$, for any parameter $δ\in \mathbb{C}$, is generated by the supersymmetric polynomials evaluated at the Jucys-Murphy elements. Moreover, we prove that its dimension is independent of the parameter $δ$.

math.RT↗
arXiv2023

Centers of Hecke Algebras of Complex Reflection Groups

We provide a dual version of the Geck--Rouquier Theorem on the center of an Iwahori--Hecke algebra, which also covers the complex case. For the eight complex reflection groups of rank $2$, for which the symmetrising trace conjecture is known to be true, we provide a new faithful matrix model for their Hecke algebra $H$. These models enable concrete calculations inside $H$. For each of the eight groups, we compute an explicit integral basis of the center of $H$.

math.RT↗
arXiv2022

The freeness and trace conjectures for parabolic Hecke subalgebras

The two most fundamental conjectures on the structure of the generic Hecke algebra $\mathcal{H}(W)$ associated with a complex reflection group $W$ state that $\mathcal{H}(W)$ is a free module of rank $|W|$ over its ring of definition, and that $\mathcal{H}(W)$ admits a canonical symmetrising trace. The first conjecture has recently become a theorem, while the second conjecture, known to hold for real reflection groups, has only been proved for some exceptional non-real complex reflection groups (all of rank $2$ but one). The two most fundamental conjectures on the structure of the parabolic Hecke subalgebra $\mathcal{H}(W')$ associated with a parabolic subgroup $W'$ of $W$ state that $\mathcal{H}(W)$ is a free left and right $\mathcal{H}(W')$-module of rank $|W|/|W'|$, and that the canonical symmetrising trace of $\mathcal{H}(W')$ is the restriction of the canonical symmetrising trace of $\mathcal{H}(W)$ to $\mathcal{H}(W')$. Until now, these two conjectures have only be known to be true for real reflection groups. We prove them for all complex reflection groups of rank $2$ for which the BMM symmetrising trace conjecture is known to hold.

math.RT↗
arXiv2019

Decomposition matrices for the generic Hecke algebras on 3 strands in characteristic 0

We classify all the decomposition matrices of the generic Hecke algebras on 3 strands in characteristic 0. These are the generic Hecke algebras associated to the exceptional complex reflection groups $G_4$, $G_8$ and $G_{16}$. We prove that for every choice of the parameters that define these algebras, all ordinary representations are obtained as modular reductions of irreducible representations.

math.RT↗
arXiv2019

The BMM symmetrising trace conjecture for groups $G_4,\,G_5,\,G_6,\,G_7,\,G_8$

We prove the BMM symmetrising trace conjecture for the exceptional complex reflection groups $G_4,\,G_5,\,G_6,\,G_7,\,G_8$ using a combination of algorithms programmed in different languages (C++, SAGE, GAP3, Mathematica). Our proof depends on the choice of a suitable basis for the generic Hecke algebra associated with each group.

math.RT↗
arXiv2017

The BMR freeness conjecture for the tetrahedral and octahedral families

We prove the validity of the freeness conjecture of Broué, Malle and Rouquier for the generic Hecke algebras associated to the exceptional complex reflection groups of rank 2 belonging to the tetrahedral and octahedral families, and we give a description of the basis similar to the classical case of the finite Coxeter groups.

math.RT↗
arXiv2016

The Broué-Malle-Rouquier conjecture for the exceptional groups of rank 2

Between 1994 and 1998, the work of M. Broué, G. Malle, and R. Rouquier generalized in a natural way the definition of the Hecke algebra associated to a finite Coxeter group, for the case of an arbitrary complex reflection group. Attempting to also generalize the properties of the Coxeter case, they stated a number of conjectures concerning these Hecke algebras. One specific example of importance regarding those yet unsolved conjectures is the so-called BMR freeness conjecture. This conjecture is known to be true apart from 16 cases, that are almost all the exceptional groups of rank 2. These exceptional groups of rank 2 fall into three families: the tetrahedral, octahedral and icosahedral family. We prove the validity of the BMR freeness conjecture for the exceptional groups belonging to the first two families, using a case-by-case analysis and we give a nice description of the basis, similar to the classical case of the finite Coxeter groups. We also give a new consequence of this conjecture, by obtaining the classification of irreducible representations of the braid group on 3 strands in dimension at most 5, recovering results of Tuba and Wenzl.

math.RT↗
arXiv2016

Universal deformations of the finite quotients of the braid group on 3 strands

We prove that the quotients of the group algebra of the braid group on 3 strands by a generic quartic and quintic relation respectively, have finite rank. This is a special case of a conjecture by Broué, Malle and Rouquier for the generic Hecke algebra of an arbitrary complex reflection group. Exploring the consequences of this case, we will prove that we can determine completely the irreducible representations of this braid group for dimension at most 5, thus reproving a classification of Tuba and Wenzl in a more general framework.

math.RT↗