Publicaties
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A new construction of Moufang quadrangles of type E6, E7 and E8 Universiteit Gent
Multiparameter Quantum Cauchy-Binet Formulas Vrije Universiteit Brussel
The quantum Cayley-Hamilton theorem for the generator of the reflection equation algebra has been proven by Pyatov and Saponov, with explicit formulas for the coefficients in the Cayley-Hamilton formula. However, these formulas do not give an easy way to compute these coefficients. Jordan and White provided an elegant formula for the coefficients given with respect to the generators of the reflection equation algebra. In this paper, we ...
A course on Moufang sets Universiteit Gent
A Schrodinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra D(2, 1; alpha) Universiteit Gent
We construct two infinite-dimensional irreducible representations for D(2, 1; alpha): a Schrodinger model and a Fock model. Further, we also introduce an intertwining isomorphism. These representations are similar to the minimal representations constructed for the orthosymplectic Lie supergroup and for Hermitian Lie groups of tube type. The intertwining isomorphism is the analogue of the Segal-Bargmann transform for the orthosymplectic Lie ...
Local Moufang sets Universiteit Gent
All known Moufang sets arise, in some way or another, from an algebraic structure which can be called `division' in some way. In this PhD dissertation, I made an attempt to develop a theory of local Moufang sets, which generalize Moufang sets in a way to allow constructing using the corresponding local algebraic structures. In the first of the two major parts of the dissertation, I develop the theory of local Moufang sets, while in the second ...
Green rings of pointed rank one Hopf algebras of non-nilpotent type Universiteit Hasselt
In this paper, we continue our study of the Green rings of finite dimensional pointed Hopf algebras of rank one initiated in [22], but focus on those Hopf algebras of non-nilpotent type. Let H be a finite dimensional pointed rank one Hopf algebra of non-nilpotent type. We first determine all non-isomorphic indecomposable H -modules and describe the Clebsch–Gordan formulas for them. We then study the structures of both the Green ring r(H) and the ...
Green Rings of Pointed Rank One Hopf Algebras of Nilpotent Type Universiteit Hasselt
Let H be a finite dimensional pointed rank one Hopf algebra of nilpotent type. We first determine all finite dimensional indecomposable H-modules up to isomorphism, and then establish the Clebsch-Gordan formulas for the decompositions of the tensor products of indecomposable H-modules by virtue of almost split sequences. The Green ring r(H) of H will be presented in terms of generators and relations. It turns out that the Green ring r(H) is ...
Bicrossed products for finite groups Vrije Universiteit Brussel
We investigate two questions regarding bicrossed products of finite groups which we believe have the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The first one is the problem of classifying groups which can be written as bicrossed products between groups of fixed isomorphism types and the second is the problem of classifying the groups which cannot be obtained as bicrossed products of smaller ...
Monodromy Jordan blocks, b-functions and poles of zeta functions for germs of plane curves KU Leuven
We study the poles of several local zeta functions: the Igusa, topological and motivic zeta function associated to a germ of a holomorphic function in two variables. It was known that there is at most one double pole for (any of) these zeta functions which is then given by the log canonical threshold of the function at the singular point. If the germ is reduced Loeser showed that such a double pole always induces a monodromy eigenvalue with a ...