Irreducible projective representations of finite groups

The purpose of this paper is to prove a result on the number of irreducible projective representations of a finite group with respect to a given factor set and a group of linear characters acting on them. It includes a determination of the number of classes of projectively equivalent representations as well as a result of M. Osima on the classes of linearly equivalent representations. Osima proved his result by defining and calculating on irreducible projective Brauer characters, whereas the method used here is based on Brauer's well-known result for the linear modular representations and an induction argument on suitable coverings.     

Homotopy groups of moduli spaces of representations

We calculate certain homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups and . Our approach relies on the interpretation of these representations in terms of Higgs bundles and uses Bott-Morse theory on the corresponding moduli spaces.     

Induced representations and finite volume homogeneous spaces

We prove that the representation of $\text{C}{}^1\text{(G ×}\text{G}\text{H}\text{)}$ induced from the restriction to H of a unitary representation π of G can be constructed directly from π in the framework of Rieffel's theory of induced representations of C¹-algebras, with the inducing process defined by a generalized conditional expectation. We then show, in the general context of Rieffel's theory, that if the induced representation is CCR, so is the original. In a more special situation, which still generalizes that of a conditional expectation onto a subalgebra, and which includes the operation of inducing from an open subgroup and the above-mentioned process when $\text{G}\text{H}$ is of finite volume, we prove that if the induced representation is type I, so is the original, and obtain a result on intertwining operators. This provides a unified treatment, as well as an extension to the nonseparable case, of certain known results on induction and restriction of representations.     

Invariants of classCk for finite coxeter groups and their representations in terms of anisotropic spaces

This article is devoted to the study of representations of C^k { } functions f invariant with respect to finite Coxeter groups W in the form f=F op, where p is a base in the algebra of W-invariant polynomials. We examine the lowering of smoothness of F as compared with f and conclude that this lowering has an anisotropic nature and that, more precisely, at each point Po it is described by a vector { }. We examine the cases W=A_n, B_n, D_n, { }; in each case the greatest component { } of { } is equal to the Coxeter number of the stabilizer W_yo of the point yo, where po=p(yo). Bibliography: 22 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 46–70. Translated by S. Yu. Pilyugin.     

Kernels of projective representations of finite groups

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 55, pp. 34–49, 1991.     

Categorical actions on unipotent representations of finite unitary groups

Publications mathématiques de l'IHÉS - Using Harish-Chandra induction and restriction, we construct a categorical action of a Kac-Moody algebra on the category of unipotent...     

Minimal permutation representations of finite simple orthogonal groups

In the paper, nontrivial permutation representations of minimal degree are studied for finite simple orthogonal groups. For them, we find degrees, ranks, subdegrees, point stabilizers and their pairwise intersections.Translated fromAlgebra i Logika, Vol. 33, No. 6, pp. 603–627, November–December, 1994.