Related papers: Representations of Quantum Groups defined over Com…
We classify the irreducible projective representations of symmetric and alternating groups of minimal possible and second minimal possible dimensions, and get a lower bound for the third minimal dimension. On the way we obtain some new…
A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions of quantum groups, and proofs of the…
In this paper we extend the relation between convolutional codes and linear systems over finite fields to certain commutative rings through first order representations . We introduce the definition of rings with representations as those for…
This is a continuation of an earlier preprint (math.GT/0209121) under the same title. These papers grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or…
This is a survey on the transitive quantum groups $G\subset S_N^+$, and on the flat matrix models $\pi:C(G)\to M_N(C(X))$ for the corresponding Hopf algebras. We review the known results on the subject, with a number of improvements,…
The paper contains the derivation of a general set of recurrence formulas for the calculus of the SU(3) Clebsch-Gordan coefficients. The first six sections are introductory, presenting the notations and placing SU(3) in the framework of the…
We present a survey of recent results, scattered in a series of papers that appeared during past five years, whose common denominator is the use of cubic relations in various algebraic structures. Cubic (or ternary) relations can represent…
In this note we give some new results concerning the subgroup commutativity degree of a finite group $G$. These are obtained by considering the minimum of subgroup commutativity degrees of all sections of $G$.
We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a…
We give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.
The paper presents some new results on Z-related sets obtained by computational methods. We give a complete enumeration of all Z-related sets in $\mathbb{Z}_{N}$ for small $N$. Furthermore, we establish that there is a reasonable…
We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neumann regular rings, C*-algebras, and complemented modular lattices. We prove additional…
This is the third chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.
We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
We examine a few problems of enumerative geometry and present their solutions in the framework of deformed (quantum) cohomology rings.
We introduce the concept of a partial abstract kernel associated to a group G and a semilattice of groups A and relate the partial cohomology group H^3(G,C(A)) with the obstructions to the existence of admissible extensions of A by G which…
We give the full representation theory of the gravitational extended corner symmetry group in two-dimensions. This includes projective representations, which correspond to representations of the quantum corner symmetry group. We find that…
Structural properties of unitary groups over local, not necessarily commutative, rings are developed, with applications to the computation of the orders of these groups (when finite) and to the degrees of the irreducible constituents of the…
We classify semisimple module categories over the tensor category of representations of quantum SL(2) extending previous results to the roots of unity and positive characteristic cases.