Related papers: Induced Representations of Cayley-Klein Orthogonal…
We define and investigate the concept of the groupoid representation induced by a representation of the isotropy subgroupoid. Groupoids in question are locally compact transitive topological groupoids. We formulate and prove the…
Let V be an Harish-Chandra discrete series representation of a real semi-simple Lie group G' and let G be a semi-simple subgroup of G'. In this paper, we give a geometric expression of the G-multiplicities in V when the representation V is…
We survey different tools to classify representations of compact Lie groups according to their cohomogeneity and apply these methods to the case of irreducible representations of cohomogeneity 6, 7 and 8.
In the recent paper [AF12], we introduced an analysis of the Brylinski-Kostant model for spherical minimal representations for simple real Lie groups of non Hermitian type. We generalize here that analysis and give a unified geometric…
Given an orthogonal representation of a compact group, we show that any element of the connected component of the isometry group of the orbit space lifts to an equivariant isometry of the original Euclidean space. Corollaries include a…
We construct a family of orthogonal characters of an algebra group which decompose the supercharacters defined by Diaconis and Isaacs. Like supercharacters, these characters are given by nonnegative integer linear combinations of Kirillov…
The extension of FRT quantization theory for the nonsemisimple CK groups is suggested. The quantum orthogonal CK groups are realized as the Hopf algebras of the noncommutative functions over an associative algebras with nilpotent…
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
It is known that every real orthogonal matrix can be brought into the domain of the Cayley transform by multiplication with a suitable diagonal signature matrix. In this paper we provide a constructive and numerically efficient algorithm…
All unitary irreducible representations of centrally extended (N-odd) N-conformal Galilei group are constructed. The "on-shell" action of the group is derived and shown to coincide, in special but most important case, with that obtained in:…
The problem of construction of irreducible representations of quantum $A^q_n$ algebras is solved at the level of explicit integration of the linear (inhomogeneous) system in finite differences in the n-dimensional space. The general…
We continue our work on understanding Howe correspondences by using theta representations from p-adic groups to compact groups. We prove some results for unitary theta representations of compact groups with respect to the induction and…
We revisit the classifications of classical and quantum galilean particles: that is, we fully classify homogeneous symplectic manifolds and unitary irreducible projective representations of the Galilei group. Equivalently, these are…
Hypercubic groups in any dimension are defined and their conjugate classifications and representation theories are derived. Double group and spinor representation are introduced. A detailed calculation is carried out on the structures of…
We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…
We show that the class of inductive limits of the representations of finite symmetric groups with simple spectrum coinsides with the class of Markov representations of the infinite symmetric group associated with Markov measures on the…
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…
In this paper we study the variety of one dimensional representations of a finite $W$-algebra attached to a classical Lie algebra, giving a precise description of the dimensions of the irreducible components. We apply this to prove a…
We study the representations of the infinite symmetric group induced from the identity representations of Young subgroups. It turns out that such induced representations can be either of type~I or of type~II. Each Young subgroup corresponds…
We classify the irreducible unitary modules in category O for the rational Cherednik algebras of type G(r,1,n) and give explicit combinatorial formulas for their graded characters. More precisely, we produce a combinatorial algorithm…