Related papers: Sine functions on hypergroups
Matrix elements and spherical functions of irreducible representations of the de Sitter group are studied on the various homogeneous spaces of this group.
Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…
We study invariance properties of Colombeau generalized functions under actions of smooth Lie transformation groups. Several characterization results analogous to the smooth setting are derived and applications to generalized rotational…
We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with…
We establish the functorial transfer of generic, automorphic representations from the quasi-split general spin groups to general linear groups over arbitrary number fields, completing an earlier project. Our results are definitive and, in…
Given a commutative ring with identity $R$, many different and interesting operations can be defined over the set $H_R$ of sequences of elements in $R$. These operations can also give $H_R$ the structure of a ring. We study some of these…
In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.
We discuss some natural maps from a unitary group U(n) to a smaller group U(n-m) (these maps are versions of the Livshic characteristic function). We calculate explicitly the direct images of the Haar measure under some maps. We evaluate…
We study the generalization of noncommutative gauge theories to the case of orthogonal and symplectic groups. We find out that this is possible, since we are allowed to define orthogonal and symplectic subgroups of noncommutative unitary…
In the present paper we introduce a commutative hypergroup associated with a hyperfield of a compact commutative hypergroup based on a discrete commutative hypergroup. Moreover we investigate the dual hyperfield and show the dual relation.…
In this paper we study multilinear morphisms between commutative group schemes and the associated tensor constructions. We will also do some explicit calculations and give examples that show that this theory behaves in a way that one would…
By an additive action on a hypersurface H in the projective space P^{n+1} we mean an effective action of a commutative unipotent group on P^{n+1} which leaves H invariant and acts on H with an open orbit. Brendan Hassett and Yuri Tschinkel…
In this paper, we consider various graphs, namely: power graph, cyclic graph, enhanced power graph and commuting graph, on a finite semigroup $S$. For an arbitrary pair of these four graphs, we classify finite semigroups such that the…
We introduce some classical concepts in the representation theory of compact groups, in order to use them for a new generalization of the Peter-Weyl Theorem. We mostly deal with functions on locally compact groups possessing large…
We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using…
We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group $G$ as their expansions into series of special functions that are invariant under the action of the even…
Quasisymmetric functions in superspace were introduced as a natural extension of classical quasisymmetric functions involving both commuting and anticommuting variables. In this paper, we first provide a characterization of the algebra of…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
For each finite classical group $G$, we classify the subgroups of $G$ which act transitively on a $G$-invariant set of subspaces of the natural module, where the subspaces are either totally isotropic or nondegenerate. Our proof uses the…
Characteristic functions of linear operators are analytic functions that serve as complete unitary invariants. Such functions, as long as they are built in a natural and canonical manner, provide representations of inner functions on a…