共查询到20条相似文献,搜索用时 15 毫秒
1.
Xiaoping Xu 《Journal of Pure and Applied Algebra》2008,212(6):1253-1309
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
2.
A permutation representation of a finite group is multiplicity-free if all the irreducible constituents in the permutation character are distinct. There are three main reasons why these representations are interesting: it has been checked that all finite simple groups have such permutation representations, these are often of geometric interest, and the actions on vertices of distance-transitive graphs are multiplicity-free. In this paper we classify the primitive multiplicity-free representations of the sporadic simple groups and their automorphism groups. We determine all the distance-transitive graphs arising from these representations. Moreover, we obtain intersection matrices for most of these actions, which are of further interest and should be useful in future investigations of the sporadic simple groups. 相似文献
3.
The irreducible representations of a simple three-dimensional Lie algebra over a field of finite characteristic are enumerated. The dimensionalities of all representations do not exceed the characteristics p of the base field. For any dimensionality< p there exists a unique representation of this dimensionality. The representations of dimensionality p form a three-dimensional algebraic set. Six literature references are cited.Translated from Matematicheskie Zametki, Vol. 2, No. 5, pp. 439–454, November, 1967. 相似文献
4.
XI NanHua 《中国科学 数学(英文版)》2014,57(6):1109-1120
In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps. 相似文献
5.
A. I. Shtern 《Journal of Mathematical Sciences》2004,123(4):4324-4339
We prove that irreducible unitary representations of the discrete series of simple Hermitian-symmetric Lie groups can be continuously deformed in the class of pure unitary pseudo-representations (note that these representations cannot be continuously deformed in the class of unitary representations). We also briefly recall the main definitions and facts related to the notions of quasi-symmetry and pseudo-symmetry and to the realization of representations of the holomorphic discrete series of simple hermitian-symmetric Lie groups. 相似文献
6.
Xiaoli Kong 《代数通讯》2013,41(6):2177-2183
The baby Tits–Kantor–Koecher (TKK) algebra constructed from the smallest (nonlattice) semilattice is related to the “smallest” extended affine Lie algebras other than the finite dimensional simple Lie algebras and the affine Kac–Moody algebras. In this article, we classify the finite dimensional irreducible representations for the baby TKK algebra. It turns out that such representations can be lifted from modules of direct sums of finitely many copies of the simple Lie algebra sp 4(?). 相似文献
7.
R. V. Moody L. Motlochová J. Patera 《Journal of Fourier Analysis and Applications》2014,20(6):1257-1290
Lie groups with two different root lengths allow two ‘mixed sign’ homomorphisms on their corresponding Weyl groups, which in turn give rise to two families of hybrid Weyl group orbit functions and characters. In this paper we extend the ideas leading to the Gaussian cubature formulas for families of polynomials arising from the characters of irreducible representations of any simple Lie group, to new cubature formulas based on the corresponding hybrid characters. These formulas are new forms of Gaussian cubature in the short root length case and new forms of Radau cubature in the long root case. The nodes for the cubature arise quite naturally from the (computationally efficient) elements of finite order of the Lie group. 相似文献
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For certain nilpotent real Lie groups constructed as semidirect products, algebras of invariant differential operators on some coadjoint orbits are used in the study of boundedness properties of the Weyl–Pedersen calculus of their corresponding unitary irreducible representations. Our main result is applicable to all unitary irreducible representations of arbitrary 3-step nilpotent Lie groups. 相似文献
11.
Jens Carsten Jantzen 《Mathematische Zeitschrift》2013,275(1-2):569-594
Consider a finite dimensional restricted Lie algebra over a field of prime characteristic. Each linear form on this Lie algebra defines a finite dimensional quotient of its universal enveloping algebra, called a reduced enveloping algebra. This leads to a Cartan matrix recording the multiplicities as composition factors of the simple modules in the projective indecomposable modules for such a reduced enveloping algebra. In this paper we show how to compare such Cartan matrices belonging to distinct linear forms. As an application we rederive and generalise the reciprocity formula first discovered by Humphreys for Lie algebras of reductive groups. For simple Lie algebras of Cartan type we see, for example, that the Cartan matrices for linear forms of non-positive height are submatrices of the Cartan matrix for the zero linear form. 相似文献
12.
Alexander N. Rudy 《Central European Journal of Mathematics》2005,3(4):606-613
The paper deals with the real classical Lie algebras and their finite dimensional irreducible representations. Signature formulae
for Hermitian forms invariant relative to these representations are considered. It is possible to associate with the irreducible
representation a Hurwitz matrix of special kind. So the calculation of the signatures is reduced to the calculation of Hurwitz
determinants. Hence it is possible to use the Routh algorithm for the calculation. 相似文献
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G. V. Voskresenskaya 《Mathematical Notes》1992,52(1):649-654
This paper considers the restriction of adjoint representations of simple Lie groups whose algebras are of even rank to finite subgroups in which each element has a rational characteristic polynomial. The nature of the virtual characters that appear is explained.Translated from Matematicheskie Zametki, Vol. 52, No. 1, pp. 25–31, July, 1992. 相似文献
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Let Uε(g) be the simply connected quantized enveloping
algebra at roots of one associated to a finite
dimensional complex simple Lie algebra g.
The De Concini-Kac-Procesi conjecture on the
dimension of the irreducible representations of Uε(g)
is proved for the representations corresponding to the
spherical conjugacy classes of the simply connected
algebraic group G with Lie algebra g. We
achieve this result by means of a new characterization
of the spherical conjugacy classes of G in terms of
elements of the Weyl group. 相似文献
17.
Karl M. Peters 《代数通讯》2013,41(12):4807-4826
In this paper, we analyze the characters of modular, irreducible rep-resentations of classical Lie algebras g of types Al-1 and Ci arising from a characteristic 0 construction of torsion free representations. By character, we refer to linear functionals on g identified with algebra homomorphisms from a distinguished central subalgebra O of the universal enveloping algebra of g. If Lie(G') = g, then for each character X standard representatives with respect to a fixed toral subalgebra are found in the (2-orbit containing the character X For many parameters, these characters are nilpotent. Furthermore, modular representations of type Al-1 and type Cl Lie algebras constructed by induction from these irreducible, torsion free representations are shown to admit characters in a family of both Richardson and non-Richardson nilpotent orbits. Through this explicit induction construction, irreducible representations of minimal p-power dimension under the Kac-Weisfeiler conjecture are realized 相似文献
18.
A. U. Klimyk 《Mathematical Notes》1974,16(5):1033-1037
The problem of the decomposition of the tensor product of finite and infinite representations of a complex semigroup of a Lie group is examined by using the theory of characters of completely irreducible representations. A theorem is proved which indicates that completely irreducible representations enter into the expansion of the tensor product of a finite and elementary representation.Translated from Matematicheskie Zametki, Vol. 16, No. 5. pp. 731–739, November, 1974. 相似文献
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Hans Tilgner 《Linear and Multilinear Algebra》1977,5(1):27-31
Any two representations of dimensions n resp. r of a given group G allow the construction of a third representation φ in the space of rectangular n × r matrices Kn,r over the same ground field K. The φ-semidirect product of Kn,r and G then has (n + r) dimensional representation. The inhomogenizations of G and in case of matrix Lie groups G the tangent groups are special cases of this construction. The contragredient as well as the Lie algebraical versions of these results are included. In the final section the construction is generalized to symmetric spaces and their local algebraical structures, the Lie triples, by defining semidirect products resp. semidirect sums with respect to a representation 相似文献