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1.
The notion of globally irreducible representations of finite groups has been introduced by B. H. Gross, in order to explain new series of Euclidean lattices discovered recently by N. Elkies and T. Shioda using Mordell--Weil lattices of elliptic curves. In this paper we first give a necessary condition for global irreducibility. Then we classify all globally irreducible representations of L 2(q) and 2B2(q), and of the majority of the 26 sporadic finite simple groups. We also exhibit one more globally irreducible representation, which is related to the Weil representation of degree (pn-1)/2 of the symplectic group Sp2n(p) (p 1 (mod 4) is a prime). As a consequence, we get a new series of even unimodular lattices of rank 2(pn–1). A summary of currently known globally irreducible representations is given.  相似文献   

2.
The notion ofglobally irreducible representations of finite groups was introduced by B. H. Gross, in order to explain new series of Euclidean lattices discovered by N. Elkies and T. Shioda using Mordell-Weil lattices of elliptic curves. In this paper we classify all globally irreducible representations coming from projective complex representations of the finite simple groups PSL3(q) and PSU3(q). The main result is that these representations are essentially those discovered by Gross.  相似文献   

3.
The wreath product of finite association schemes is a natural generalization of the notion of the wreath product of finite permutation groups. We determine all irreducible representations (the Jacobson radical) of a wreath product of two finite association schemes over an algebraically closed field in terms of the irreducible representations (Jacobson radicals) of the two factors involved.  相似文献   

4.
The classification of irreducible square integrable representations of classical -adic groups is completed in this paper, under a natural local assumption. Further, this classification gives a parameterization of irreducible tempered representations of these groups. Therefore, it implies a classification of the non-unitary duals of these groups (modulo cuspidal data). The classification of irreducible square integrable representations is directly related to the parameterization of irreducible square integrable representations in terms of dual objects, which is predicted by Langlands program.

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5.
The main aim of the paper is to study infinite-dimensional representations of the real form U q (u n, 1) of the quantized universal enveloping algebra U q (gl n + 1). We investigate the principal series of representations of U q (u n, 1) and calculate the intertwining operators for pairs of these representations. Some of the principal series representations are reducible. The structure of these representations is determined. Then we classify irreducible representations of U q (u n, 1) obtained from irreducible and reducible principal series representations. All *-representations in this set of irreducible representations are separated. Unlike the classical case, the algebra U q (u n, 1) has finite-dimensional irreducible *-representations.  相似文献   

6.
Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups (G-groups). In this paper we establish a decomposition theorem for irreducible G-groups which expresses a suitable irreducible G-group as a tensor product of two projective G-groups in a similar way to the celebrated theorem of Clifford for linear representations. Moreover, we study the non-abelian minimal normal subgroups of G in which this decomposition is possible.  相似文献   

7.
In this paper, we give a new formulation of a geometric lemma for the metaplectic groups over p-adic field F, analogous to the existing one for classical groups. This enables us to give a Zelevinsky type classification of irreducible admissible genuine representations of metaplectic groups. As an application of our Jacquet module technique, we explicitly calculate Jacquet modules of even and odd Weil representations.  相似文献   

8.
We obtain a complete classification of the continuous unitary representations of oligomorphic permutation groups (those include the infinite permutation group S ??, the automorphism group of the countable dense linear order, the homeomorphism group of the Cantor space, etc.). Our main result is that all irreducible representations of such groups are obtained by induction from representations of finite quotients of open subgroups and, moreover, every representation is a sum of irreducibles. As an application, we prove that many oligomorphic groups have property (T). We also show that the Gelfand?CRaikov theorem holds for topological subgroups of S ??: for all such groups, continuous irreducible representations separate points in the group.  相似文献   

9.
Tushev  A. V. 《Mathematical Notes》2002,72(1-2):117-128
We show, in particular, that in the class of minimax two-step nilpotent groups only finitely generated groups can admit exact irreducible primitive representations over a finitely generated field of characteristic zero. We also suggest some approaches to studying induced representations of nilpotent groups of finite rank.  相似文献   

10.
11.
We define exact functors from categories of Harish–Chandra modules for certain real classical groups to finite-dimensional modules over an associated graded affine Hecke algebra with parameters. We then study some of the basic properties of these functors. In particular, we show that they map irreducible spherical representations to irreducible spherical representations and, moreover, that they preserve unitarity. In the case of split classical groups, we thus obtain a functorial inclusion of the real spherical unitary dual (with “real infinitesimal character”) into the corresponding p-adic spherical unitary dual.  相似文献   

12.
We continue the study of glider representations of finite groups G with given structure chain of subgroups e ? G 1 ?… ? G d = G. We give a characterization of irreducible gliders of essential length ed which in the case of p-groups allows to prove some results about classical representation theory. The paper also contains an introduction to generalized character theory for glider representations and an extension of the decomposition groups in the Clifford theory. Furthermore, we study irreducible glider representations for products of groups and nilpotent groups.  相似文献   

13.
《代数通讯》2013,41(4):1777-1797
Abstract

In this paper we introduce and study the local quiver as a tool to investigate the étale local structure of moduli spaces of θ-semistable representations of quivers. As an application we determine the dimension vectors associated to irreducible representations of the torus knot groups G p,q  = ?a, b ∣ a  p  = b q ?.  相似文献   

14.
We construct irreducible modules of centrally-extended classical Lie algebras over left ideals of the algebra of differential operators on the circle, through certain irreducible modules of centrally-extended classical Lie algebras of infinite matrices with finite number of nonzero entries. The structures of vertex algebras associated with the vacuum representations of these algebras are determined. Moreover, we prove that under certain conditions, the highest-weight irreducible modules of centrally-extended classical Lie algebras of infinite matrices with finite number of nonzero entries naturally give rise to the irreducible modules of the simple quotients of these vertex algebras. From vertex algebra and its representation point of view, our results with positive integral central charge are high-order differential operator analogues of the well-known WZW models in conformal field theory associated with affine Kac-Moody algebras. Indeed, when the left ideals are the algebra of differential operators, our Lie algebras do contain affine Kac-Moody algebras as subalgebras and our results restricted on them are exactly the representation contents in WZW models. Similar results with negative central charge are also obtained.  相似文献   

15.
We consider a new method for constructing finite-dimensional irreducible representations of the reflection equation algebra. We construct a series of irreducible representations parameterized by Young diagrams. We calculate the spectra of central elements s k=Trq L k of the reflection equation algebra on q-symmetric and q-antisymmetric representations. We propose a rule for decomposing the tensor product of representations into irreducible representations.  相似文献   

16.
17.
Wadii Hajji 《代数通讯》2013,41(12):5261-5281
The aim in this article is to provide a parametrization of the finite dimensional irreducible representations of a compact inverse semigroup in terms of the irreducible representations of maximal subgroups and order theoretic properties of the idempotent set. As a consequence, we obtain a new, and more conceptual, proof of the following theorem of Shneperman: a compact inverse semigroup has enough finite dimensional irreducible representations to separate points if and only if its idempotent set is totally disconnected. Moreover, we also prove that every norm continuous irreducible *-representation of a compact inverse semigroup on a Hilbert space is finite dimensional.  相似文献   

18.
We define a new class of racks, called finitely stable racks, which, to some extent, share various flavors with Abelian groups. Characterization of finitely stable Alexander quandles is established. Further, we study twisted rack dynamical systems, construct their cross-products, and introduce representation theory of racks and quandles. We prove several results on the strong representations of finite connected involutive racks analogous to the properties of finite Abelian groups. Finally, we define the Pontryagin dual of a rack as an Abelian group which, in the finite involutive connected case, coincides with the set of its strong irreducible representations.  相似文献   

19.
This paper analyzes the space HomH(, 1), where is an irreducible, tame supercuspidal representation of GL(n) over a p-adic field and H is a unitary group in n variables contained in GL(n). It is shown that this space of linear forms has dimension at most one. The representations which admit nonzero H-invariant linear forms are characterized in several ways, for example, as the irreducible, tame supercuspidal representations which are quadratic base change lifts.Research supported in part by NSA grant #MDA904-99-1-0065.Research supported in part by NSERC  相似文献   

20.
We describe minimal permutation representations, i.e., faithful permutation representations of least degree, of classical finite simple groups as groups of automorphisms of simple Lie algebras.  相似文献   

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