Related papers: Diagrammatics for dicyclic groups
The multidimensional quantization procedure, proposed by the first author and its modifications (reduction to radicals and lifting on U(1)-coverings) give us a almost universal theoretical tools to find irreducible representations of Lie…
We describe a new type of polycyclic presentations, that we will call refined solvable presentations, for polycyclic groups. These presentations are obtained by refining a series of normal subgroups with abelian sections. These…
We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representations of a Lie group on a vector bundle, and related concepts, may be understood in terms of representations of Lie…
We extend the Weil representation of infinite-dimensional symplectic group to a representation a certain category of linear relations.
We consider the group algebra of the symmetric group as a superalgebra, and describe its Lie subsuperalgebra generated by the transpositions. The updated version corrects some of the arguments made in Sections 4.5 - 4.7. The statements of…
We propose a duality between quiver gauge theories and the combinatorics of dimer models. The connection is via toric diagrams together with multiplicities associated to points in the diagram (which count multiplicities of fields in the…
A cyclic subgroup graph of a group $G$ is a graph whose vertices are cyclic subgroups of $G$ and two distinct vertices $H_1$ and $H_2$ are adjacent if $H_1\leq H_2$, and there is no subgroup $K$ such that $H_1<K<H_2$. M.T\u{a}rn\u{a}uceanu…
The sandpile group of a connected graph is the group of recurrent configurations in the abelian sandpile model on this graph. We study the structure of this group for the case of regular trees. A description of this group is the following:…
Representations of braid group obtained from rational conformal field theories can be used to obtain explicit representations of Temperley-Lieb-Jones algebras. The method is described in detail for SU(2)$_k$ Wess - Zumino conformal field…
A class of subgroups is obtained for symmetric groups using signed Brauer diagrams.
As is known, any realization of SU(2) in the phase space of a dynamical system can be generalized to accommodate the exceptional supergroup $D(2,1;\alpha)$, which is the most general $\mathcal{N}{=}\,4$ supersymmetric extension of the…
Inspired by earlier works on representations of the Temperley-Lieb algebra we introduce a novel family of representations of the algebra. This may be seen as a generalization of the so called asymmetric twin representation. The underlying…
We consider the dual space of linear groups over Dynkinian and Euclidean algebras, i.e. finite dimensional algebras derived equivalent to the path algebra of Dynkin or Euclidean quiver. We prove that this space contains an open dense subset…
We provide a family of representations of GL(2n) over a p-adic field that admit a non-vanishing linear functional invariant under the symplectic group (i.e. representations that are Sp(2n)- distinguished). While our result generalizes a…
This is an expository article. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via…
We determine the image of the braid groups inside the Temperley-Lieb algebras, defined over finite field, in the semisimple case, and for suitably large (but controlable) order of the defining (quantum) parameter. We also prove that, under…
This paper presents two facets. First, we show that the periodic table of chemical elements can be described, understood and modified (as far as its format is concerned) on the basis of group theory and more specifically by using the group…
A study of triangulations of cycles in the Cayley diagrams of finitely generated groups leads to a new geometric characterization of hyperbolic groups.
Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms…
We determine the characters of SL(2) representations of groups and surface groups.