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...

We consider the continuum scaling limit of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p, p′) as ‘rational’ logarithmic conformal field theories with extendedW symmetry. The representation content is found to consist of 6pp′ − 2p− 2p′ W-indecomposable representations of which 2p+2p′ − 2 are of rank 1, 4pp′ − 2p− 2p′ are of rank 2, while the remaining 2(p− 1)(p′ −...

Abstract We begin a systematic study of unitary representations minimal W -algebras. In particular, we classify -algebras and make substantial progress in classification their irreducible highest weight modules. also compute the characters these

The goal of harmonic analysis on a (noncommutative) group is to decompose the most “natural” unitary representations of this group (like the regular representation) on irreducible ones. The infinite–dimensional unitary group U(∞) is one of the basic examples of “big” groups whose irreducible representations depend on infinitely many parameters. Our aim is to explain what the harmonic analysis o...

The characters of the irreducible representations of the symmetric group play an important role in many areas of mathematics. However, since the early work of Frobenius [5] in 1900, no explicit formula was found for them. The characters of the symmetric group were computed through various recursive algorithms, but explicit formulas were only known for about ten particular cases [5, 9]. The purp...

We give closed product formulas for the irreducible characters of symmetric groups related to rectangular `almost square' Young diagrams $p \times(p+\delta)$ a fixed value an integer $\delta$ and arbitrary $p$.

Any free presentation for the finite group G determines a central extension (R, F ) for G having the projective lifting property for G over any field k. The irreducible representations of F which arise as lifts of irreducible projective representations of G are investigated by considering the structure of the group algebra kF , which is greatly influenced by the fact that the set of torsion ele...

A Brauer character of a finite group may be lifted to an ordinary character if it lies in a block whose defect groups are contained in a normal p-solvable subgroup. By the Fong-Swan theorem [2, Theorem 72.1], an irreducible Brauer character of a finite p-solvable group G may be lifted to an ordinary (complex) character of G. In other words, every Brauer character is the restriction of some ...

The irreducible characters of a finite reductive group are partitioned into Harish-Chandra series that labelled by cuspidal pairs. In this note, we describe how one can algorithmically calculate those pairs using results Lusztig.