相关论文: Representation Growth for Linear Groups

The growth rate function $r_N$ counts the number of irreducible representations of simple complex Lie groups of dimension $N$. While no explicit formula is known for this function, previous works have found bounds for $R_N=\sum_{i=1}^Nr_i$.…

We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic…

We give a description of non-growing subsets in linear groups, which extends the Product theorem for simple groups of Lie type. We also give an account of various related aspects of growth in linear groups.

We prove that the numbers of irreducible n-dimensional complex continuous representations of the special linear groups over p-adic integers grow slower than the square of n. We deduce that the abscissas of convergence of the representation…

We study the representation growth of alternating and symmetric groups in positive characteristic and restricted representation growth for the finite groups of Lie type. We show that the the number of representations of dimension at most n…

Let G be an arithmetic lattice in a semisimple algebraic group over a number field. We show that if G has the congruence subgroup property, then the number of n-dimensional irreducible representations of G grows like n^a, where a is a…

This article examines lower bounds for the representation growth of finitely generated (particularly profinite and pro-p) groups. It also considers the related question of understanding the maximal multiplicities of character degrees in…

We calculate extensions between certain irreducible admissible representations of p-adic groups.

For a finite group $G$, the representation dimension is the smallest integer realizable as the degree of a complex faithful representation of $G$. In this article, we compute representation dimension for some $p$-groups, their direct…

In this note, we study irreducible unitary representations of special linear groups of lower ranks, in terms of the matrix models of Gelfand-Naimark and Gelfand-Graev. Review of existing literature is provided. We also add some new…

We determine the finite groups whose real irreducible representations have different degrees.

This is a survey of methods developed in the last few years to prove results on growth in non-commutative groups. These techniques have their roots in both additive combinatorics and group theory, as well as other fields. We discuss linear…

Residual finiteness growth measures how well-approximated a group is by its finite quotients. We prove that some related growth functions characterize linearity for a class of groups including all hyperbolic groups.

The main results in this thesis deal with the representation growth of certain classes of groups. In chapter $1$ we present the required preliminary theory. In chapter $2$ we introduce the Congruence Subgroup Problem for an algebraic group…

The main result of this paper is the classification of the real irreducible representations of compact Lie groups with vanishing homogeneity rank.

We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…

Answering a question of I. M. Isaacs, we show that the largest degree of irreducible complex representations of any finite non-abelian simple group can be bounded in terms of the smaller degrees. We also study the asymptotic behavior of…

This thesis is devoted to the study of the interactions existing between the algebraic structure of locally compact groups and the properties of their continuous unitary representations, with a special emphasis on the Type I groups. On the…

We consider sequences of degrees of ordinary irreducible $S_n$-characters. We assume that the corresponding Young diagrams have rows and columns bounded by some linear function of $n$ with leading coefficient less than one. We show that any…

We give a general asymptotic formula for the growth rate of the number of indecomposable summands in the tensor powers of representations of finite groups, over a field of arbitrary characteristic. In characteristic zero we obtain…