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We apply the notion of relative adjoint functor to generalise closed monoidal categories. We define representations in such categories and give their relation with left actions of monoids. The translation of these representations under lax…
Inspired by prior work of Bruinier and Ono and Mertens and Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…
Using crossed homomorphisms, we show that the category of weak representations (resp. admissible representations) of Lie-Rinehart algebras (resp. Leibniz pairs) is a left module category over the monoidal category of representations of Lie…
We consider a class of non-locally compact groups on which one may define a left-invariant, finitely additive measure taking values in some finitely generated extension of the field $\mathbb{R}$ of real numbers. In particular, we recover…
We introduce the notion of a diagram category and discuss its application to the invariant theory of classical groups and super groups, with some indications concerning extensions to quantum groups and quantum super groups. Tensor functors…
Invariants allow to classify images up to the action of a group of transformations. In this paper we introduce notions of the algebras of simultaneous polynomial and rational 2D moment invariants and prove that they are isomorphic to the…
In this paper, we define locally matchable subsets of a group which is derived from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue…
The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…
When a semigroup has a unary operation, it is possible to define two binary operations, namely, left and right division. In addition it is well known that groups can be defined in terms of those two divisions. The aim of this paper is to…
We introduce locally involutive semigroups and embed them into the category of ordered groupoids. This embedding restricts to a correspondence between quasi-involutive semigroups and ordered groupoids with mediator, extending the classical…
We introduce the new concept of cartesian module over a pseudofunctor $R$ from a small category to the category of small preadditive categories. Already the case when $R$ is a (strict) functor taking values in the category of commutative…
The aim of this note is to prove a representation theorem for left--invariant functionals in Carnot groups. As a direct consequence, we can also provide a $\Gamma$-convergence result for a smaller class of functionals.
We study selfadjoint functors acting on categories of finite dimensional modules over finite dimensional algebras with an emphasis on functors satisfying some polynomial relations. Selfadjoint functors satisfying several easy relations, in…
We study the relative growth of finitely generated subgroups in finitely generated groups, and the corresponding distortion function of the embeddings. We explore which functions are equivalent to the relative growth functions and…
We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…
We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix…
This thesis is devoted to algorithmic aspects of the implementation of Cartan's moving frame method to the problem of the equivalence of submanifolds under a Lie group action. We adopt a general definition of a moving frame as an…
After explaining the concepts of Langlands dual and miniscule representations, we define an analog of the Gauss sum for any compact, simple Lie group with a simply laced Lie algebra. We then show a reciprocity property when a Lie group is…
For any discrete group $\Gamma$ and any 2-dimensional complex representation $\rho$ of $\Gamma$, we introduce the notion of $\rho-$equivariant functions, and we show that they are parameterized by vector-valued modular forms. We also…