16 citations · 60 across the 16 of their papers we have counts for
16 papers
Complex Hadamard Matrices - Quantum Symmetries, Equivalence and Non-Local Games
Michael Brannan, Daniel Gromada, Roberto Hernández Palomares +1
We consider quantum group generalizations of the action of monomial matrices on complex Hadamard matrices. This gives rise to various notions of quantum symmetries and quantum equi…
A quantum Frucht's theorem and quantum automorphisms of quantum Cayley graphs
Michael Brannan, Daniel Gromada, Junichiro Matsuda +2
We establish a quantum version of Frucht's Theorem, proving that every finite quantum group is the quantum automorphism group of an undirected finite quantum graph. The constructio…
Quantum association schemes
Daniel Gromada
We introduce quantum association schemes. This allows to define distance regular and strongly regular quantum graphs. We bring examples thereof. In addition, we formulate the duali…
Quantum symmetries of Hadamard matrices
Daniel Gromada
We define quantum automorphisms and isomorphisms of Hadamard matrices. We show that every Hadamard matrix of size has quantum symmetries and that all Hadamard matrices of…
Some examples of quantum graphs
Daniel Gromada
We summarize different approaches to the theory of quantum graphs and provide several ways to construct concrete examples. First, we classify all undirected quantum graphs on the q…
Presentations of projective quantum groups
Daniel Gromada
Given an orthogonal compact matrix quantum group defined by intertwiner relations, we characterize by relations its projective version. As a sample application, we prove that $PU_n…
Quantum symmetries of Cayley graphs of abelian groups
Daniel Gromada
We study Cayley graphs of abelian groups from the perspective of quantum symmetries. We develop a general strategy for determining the quantum automorphism groups of such graphs. A…
Free quantum analogue of Coxeter group
Daniel Gromada
We define the quantum group -- a free quantum version of the demihyperoctahedral group (the smallest representative of the Coxeter series ). In order to do so, we…
Group-theoretical graph categories
Daniel Gromada
The semidirect product of a finitely generated group dual with the symmetric group can be described through so-called group-theoretical categories of partitions (covers only a spec…
Gluing compact matrix quantum groups
Daniel Gromada
We study glued tensor and free products of compact matrix quantum groups with cyclic groups -- so-called tensor and free complexifications. We characterize them by studying their r…
New products and -extensions of compact matrix quantum groups
Daniel Gromada, Moritz Weber
There are two very natural products of compact matrix quantum groups: the tensor product and the free product . We define a number of further products interpolatin…
Generating linear categories of partitions
Daniel Gromada, Moritz Weber
We present an algorithm for approximating linear categories of partitions (of sets). We report on concrete computer experiments based on this algorithm which we used to obtain firs…
Intertwiner spaces of quantum group subrepresentations
Daniel Gromada, Moritz Weber
We consider compact matrix quantum groups whose -dimensional fundamental representation decomposes into an -dimensional and a one-dimensional subrepresentation. Even if w…
Classification of Globally Colorized Categories of Partitions
Daniel Gromada
Set partitions closed under certain operations form a tensor category. They give rise to certain subgroups of the free orthogonal quantum group , the so called easy quantum…
On classification of Lie algebra realizations
Daniel Gromada, Severin Pošta
We study realizations of Lie algebras by vector fields. A correspondence between classification of transitive local realizations and classification of subalgebras is generalized to…
Representations of Askey--Wilson algebra
Daniel Gromada, Severin Pošta
We deal with the classification problem of finite-dimensional representations of so called Askey--Wilson algebra in the case when is not a root of unity. We classify all repres…