Abel Lacabanne

activity

20182026

collaborators

6 papers

math.RT2026

On the computation of the canonical basis for irreducible highest weight $U_{q} (gl_{\infty})$ -module

Nicolas Jacon, Abel Lacabanne

We study canonical basis elements in higher-level Fock spaces associated with the quantum group $U_{q} (gl_{\infty})$ , which are conjecturally related to Calogero-Moser theor…

math.RT2022

On Calogero-Moser cellular characters for imprimitive complex reflection groups

Nicolas Jacon, Abel Lacabanne

We study the relationship between Calogero-Moser cellular characters and characters defined from vectors of a Fock space of type $A_{\infty}$ . Using this interpretation, we show th…

math.QA2020

Fourier matrices for $G (d, 1, n)$ from quantum general linear groups

Abel Lacabanne

We construct a categorification of the modular data associated with every family of unipotent characters of the spetsial complex reflection group $G (d, 1, n)$ . The construction of th…

math.RT2020

On a conjecture about cellular characters for the complex reflection group $G (d, 1, n)$

Abel Lacabanne

We propose a conjecture relating two different sets of characters for the complex reflection group $G (d, 1, n)$ . From one side, the characters are afforded by Calogero-Moser cells, a…

math.QA2019

Crossed $S$ -matrices and Fourier matrices for Coxeter groups with automorphism

Abel Lacabanne

We study crossed $S$ -matrices for braided $G$ -crossed categories and reduce their computation to a submatrix of the de-equivariantization. We study the more general case of a categ…

math.QA2018

Drinfeld double of quantum groups, tilting modules and $Z$ -modular data associated to complex reflection groups

Abel Lacabanne

Generalizing Lusztig's work, Malle has associated to some imprimitive complex reflection group $W$ a set of "unipotent characters", which are in bijection of the usual unipotent ch…

On the computation of the canonical basis for irreducible highest weight Uq​(gl∞​)-module

On Calogero-Moser cellular characters for imprimitive complex reflection groups

Fourier matrices for G(d,1,n) from quantum general linear groups

On a conjecture about cellular characters for the complex reflection group G(d,1,n)

Crossed S-matrices and Fourier matrices for Coxeter groups with automorphism

Drinfeld double of quantum groups, tilting modules and Z-modular data associated to complex reflection groups

On the computation of the canonical basis for irreducible highest weight $U_{q} (gl_{\infty})$ -module

Fourier matrices for $G (d, 1, n)$ from quantum general linear groups

On a conjecture about cellular characters for the complex reflection group $G (d, 1, n)$

Crossed $S$ -matrices and Fourier matrices for Coxeter groups with automorphism

Drinfeld double of quantum groups, tilting modules and $Z$ -modular data associated to complex reflection groups