Related papers: Representation theory for the Kriz model
We introduce N=1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D=1+2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model…
We study the geometry and partial differential equations arising from the consideration of group-determinants, and representation theory. The simplest and most striking such example is undoubtedly that of the Humbert operator, associated…
We study the actions of a Lie group $G$ by birationally extendible automorphisms on a domain $D\subset C^n$. For a large class of such domains defined by polynomial inequalities, all automorphisms are of this type. In the cases 1) $G$ has…
As an application of the representation theory for the dihedral groups, we study the symmetric central configurations in the n-body problem where $n$ equal masses are placed at the vertices of a regular $n$-gon. Since the Hessian matrices…
We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups instead of a product of the general linear groups and by…
The main results in this thesis deal with the representation growth of certain classes of groups. In chapter $1$ we present the required preliminary theory. In chapter $2$ we introduce the Congruence Subgroup Problem for an algebraic group…
The author's recent results on spectral invariant dense subalgebras of C*-algebras associated with dynamical systems are summarized. If G is a compactly generated polynomial growth Type R Lie group, and the action of G on S(M) (Schwartz…
There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation…
In the traditional Katz-Vafa method, matter representations are determined by decomposing the adjoint representation of a parent simple Lie algebra $\mathfrak{m}$ as the direct sum of irreducible representations of a semisimple subalgebra…
We introduce two-dimensional tensor network representations of finite groups carrying a 4-cocycle index. We characterize the associated gapped (2+1)D phases that emerge when these anomalous symmetries act on tensor network ground states. We…
The earlier proposed Dynamics-Generating Approach (DGA) is reviewed and extended. Starting from an arbitrarily chosen group or semigroup which have structure similar to the structure of Galilei group, DGA allows one to construct…
After having established elementary results on the relationship between a finite complex (pseudo-)reflection group W < GL(V) and its reflection arrangement A, we prove that the action of W on A is canonically related with other natural…
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
We consider the superconformal index of class S theories of type D, which arise by compactification of the (2,0) D_n theories on a punctured Riemann surface C. We also allow for the presence of twist lines on C associated to the Z_2 outer…
We consider for two based graphs $G$ and $H$ the sequence of graphs $G_k$ given by the wedge sum of $G$ and $k$ copies of $H$. These graphs have an action of the symmetric group $\Sigma_k$ by permuting the $H$-summands. We show that the…
We present expressions for the supercurrents generated by a generic $4D,~\mathcal{N}=1$ theory of complex linear superfield $\Sigma$. We verify that these expressions satisfy the appropriate superspace conservation equations. Furthermore,…
Representations of four dimensional superconformal groups are constructed as fields on many different superspaces, including super Minkowski space, chiral superspace, harmonic superspace and analytic superspace. Any unitary irreducible…
We develop an inductive approach to the representation theory of the Yokonuma-Hecke algebra ${\rm Y}_{d,n}(q)$, based on the study of the spectrum of its Jucys-Murphy elements which are defined here. We give explicit formulas for the…
We investigate deformations of skew group algebras arising from the action of the symmetric group on polynomial rings over fields of arbitrary characteristic. Over the real or complex numbers, Lusztig's graded affine Hecke algebra and…