Related papers: Representation Theory of Polyadic Groups

Analysis of function spaces and special functions are closely related to the representation theory of Lie groups. We explain here the connection between the Laguerre functions, the Laguerre polynomials, and the Meixner-Pollacyck polynomials…

Let $G$ be a reductive $p$-adic group. We prove that all supercuspidal representations of $G$ arise through Yu's construction subject to certain hypotheses on $k$ (depending on $G$). As a corollary, under the same hypotheses, we see that…

We examine various consequences of the existence of exceptional representations of an irreducible Weyl group. (These are notes from a talk in the MIT Lie groups seminar.)

We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. We give formulas for their dimension and vertex degree. In the…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…

In this paper some reflections on the concept of transition are presented: groupoids are introduced as models for the construction of a ``generalized logic'' whose basic statements involve pairs of propositions which can be conditioned. In…

We describe representation theory of the elliptic quantum group $E_{\tau,\eta}(sl_2)$. It turns out that the representation theory is parallel to the representation theory of the Yangian $Y(sl_2)$ and the quantum loop group $ U_q(\widetilde…

We study isometric representations of the semigroup $\mathbb{Z}_+\backslash \{1\}$. Notion of an inverse representation is introduced and a complete description (up to unitary equivalence) of such representations is given. Also, we study a…

The special linear representation of a compact Lie group G is a kind of linear representation of compact Lie group G with special properties. It is possible to define the integral of linear representation and extend this concept to special…

We study the representations of the commutator subgroup of the braid group with n strands in the symmetric group of degree r. Motivated by some experimental results, we conjecture that for n>r, every such representation is trivial.

We bring a linkage from representation theory of Lie groups to homotopy theory for maps between flag manifolds. As applications we derive from representation theory abundant families of homotopy classes of maps between flag manifolds whose…

This short note is a conceptual prologue to the series of articles devoted to the analysis of interrelations between the representation theory (especially, its inverse problems) and the control and games theory.

This is the first in a series of articles devoted to providing a foundation for a theory of flocks of arbitrary cones in PG(3,q). The desire to have such a theory stems from a need to better understand the very significant and applicable…

In groups with involution a nonassociative product of elements is defined, which leads to the definition of a certain type of quasigroups. These quasigroups are represented by square tables of complex numbers, with inverses, which differ…

The theory of pictures between posets is known to encode much of the combinatorics of symmetric group representations and related topics such as Young diagrams and tableaux. Many reasons, com-binatorial (e.g. since semi-standard tableaux…

We show how a polar representation of a compact connected Lie group can be linearly determined from its dimension and isotropy subgroup data in the general reducible case.

In this book, I explored differential equations for operation in Lie group and for representations of group Lie in a vector space.

We construct a family of representations of an arbitrary variant $S_a$ of a semigroup $S$, induced by a given representation of $S$, and investigate properties of such representations and their kernels.

We introduce unitary representations of continuous groupoids on continuous fields of Hilbert spaces. We investigate some properties of these objects and discuss some of the standard constructions from representation theory in this…