The irreducible unitary representations of GL(n, ~) have been classified by D. Vogan in [V2]. In his work, four families of representations play a special role. They are (i) the one dimensional unitary representations and (ii) their complementary series; (iii) Speh's representations and (iv) their complementary series. These representations serve as "building blocks" in the sense that every irr...

For each connected real semisimple matrix group, one obtains a constructive list of the irreducible tempered unitary representations and their characters. These irreducible representations all turn out to be instances of a more general kind of representation, here called basic. The result completes Langland's classification of all irreducible admissible representations for such groups. Since no...

The correspondence between irreducible representations of the symmetric group Sn and partitions of n is well-known. Less well-known is the connection between irreducible representations of the special unitary group SU(n) and partitions with less than n parts. This paper uses this correspondence to classify the irreducible representations of SU(n) with prime power degree.

Let F be a p-adic field of characteristic 0, and let A be an F -central division algebra of dimension dA over F . In the paper we first develop the representation theory of GL(m,A), assuming that holds the conjecture which claims that unitary parabolic induction is irreducible for GL(m,A)’s. Among others, we obtain the formula for characters of irreducible unitary representations of GL(m,A) in ...

We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this problem. Furthermore, quantum Schur transforms yield efficient solutions for certain irreducible representations of the unitary group. Beyond this, we obtain poly(n...

Introduction. A great deal of work has been done in the last fifteen years on the theory and classification of irreducible unitary representations of locally compact groups. It is also generally recognized (see for example [12, § 8]) that, at least for some classes of groups, it is artificial to confine oneself to unitary representations; one ought to study the irreducible Banach space represen...

The positive-energy unitary irreducible representations of the q-deformed conformal algebra Cq = Uq(su(2, 2)) are obtained by appropriate deformation of the classical ones. When the deformation parameter q is N -th root of unity, all these unitary representations become finitedimensional. For this case we discuss in some detail the massless representations, which are also irreducible representa...

We demonstrate the main idea of constructing irreducible unitary representations of Lie groups by using Fedosov deformation quan-tization in the concrete case of the group Aff(R) of affine transformations of the real straight line. By an exact computation of the star-product and the operatorˆℓ Z , we show that the resulting representations exhausted all the irreducible representations of this g...

We give an idea of constructing irreducible unitary representations of Lie groups by using Fedosov deformation quantization in the concrete case of the group Aff(R) of affine transformations of the real line. By an exact computation of the star-product and the operator ˆ̀Z , we show that the resulting representations exhausted all the irreducible representations of this groups.