相关论文: Character formulae for classical groups

Let $G$ be a finite classical group of Lie type of rank $\ell$, defined over a field of characteristic $p>2$. In this work, we classify the irreducible representations of $G$ whose dimensions are bounded by a constant proportional to…

If $G$ is a finite group, an irreducible complex-valued character $\chi$ is called rational if $\chi(g)$ is rational for all $g\in G$. Also, a conjugacy class $x^G$ is called rational, if for all irreducible complex-valued character $\chi$,…

We give another proof of a theorem of D. Prasad (Theorem 2, \textit{Israel J. Math.} 2016), which is also a classical result of Littlewood--Richardson (Theorem VI, \textit{Q. J. Math.} 1934). For integers $m,n \ge 2$, this result calculates…

The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible $gl(m|n)$ modules. In particular, we give matrix element formulae for all gl(m|n) generators,…

Left-right and conjugation actions on matrix tuples have received considerable attention in theoretical computer science due to their connections with polynomial identity testing, group isomorphism, and tensor isomorphism. In this paper, we…

We determine explicitly the Gauss sums on the general linear group $GL_2(\mathbb{Z}/p^l\mathbb{Z})$ for all irreducible characters, where $p$ is an odd prime and $l$ is an integer > 1. While there are several studies of the Gauss sums on…

We define an analogue of the Caldero-Chapoton map (\cite{CC}) for the cluster category of finite dimensional nilpotent representations over a cyclic quiver. We prove that it is a cluster character (in the sense of \cite{Palu}) and satisfies…

Several recent problems in the representation theory of finite groups require determining whether certain characters of almost simple groups belong to the principal block. Since the values of these characters are not yet known, we employ…

This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.

In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on…

In this paper, we will show that if for every nonlinear complex irreducible character of a finite group G, some multiple of it is induced from an irreducible character of some proper subgroup of G, then G is solvable. This is a…

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…

The endoscopic classification via the stable trace formula comparison provides certain character relations between irreducible cuspidal automorphic representations of classical groups and their global Arthur parameters, which are certain…

Let B be a block of a finite group G with defect group D. We prove that the exponent of the center of D is determined by the character table of G. In particular, we show that D is cyclic if and only if B contains a "large" family of…

We establish new bounds on character values and character ratios for finite groups $G$ of Lie type, which are considerably stronger than previously known bounds, and which are best possible in many cases. These bounds have the form…

We propose a conjecture relating two different sets of characters for the complex reflection group $G(d,1,n)$. From one side, the characters are afforded by Calogero-Moser cells, a conjectural generalisation of Kazhdan-Lusztig cells for a…

Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and…

We establish a character formula for admissible unitary representations of $p$-adic almost algebraic solvable groups and we deduce the Plancherel measure in the unimodular case.

We propose and investigate a bi-infinite matrix approach to the multiplication and composition of formal Laurent series. We generalize the concept of Riordan matrix to this bi-infinite context, obtaining matrices that are not necessarily…

Let G be a finite group of order n and V an irreducible representation over the complex numbers of dimension d. For some nonnegative number e, we have n=d(d+e). If e is small, then the character of V has unusually large degree. We fix e and…