For a connected linear semisimple Lie group , this paper considers those nonzero limits of discrete series representations having infinitesimal character 0, calling them totally degenerate. Such representations exist if and only if has a compact Cartan subgroup, is quasisplit, and is acceptable in the sense of Harish-Chandra.
Totally degenerate limits of discrete series are natural objects of study in the theory of automorphic forms: in fact, those automorphic representations of adelic groups that have totally degenerate limits of discrete series as archimedean components correspond conjecturally to complex continuous representations of Galois groups of number fields. The automorphic representations in question have important arithmetic significance, but very little has been proved up to now toward establishing this part of the Langlands conjectures.
There is some hope of making progress in this area, and for that one needs to know in detail the representations of under consideration. The aim of this paper is to determine the classification parameters of all totally degenerate limits of discrete series in the Knapp-Zuckerman classification of irreducible tempered representations, i.e., to express these representations as induced representations with nondegenerate data.
The paper uses a general argument, based on the finite abelian reducibility group attached to a specific unitary principal series representation of . First an easy result gives the aggregate of the classification parameters. Then a harder result uses the easy result to match the classification parameters with the representations of under consideration in representation-by-representation fashion. The paper includes tables of the classification parameters for all such groups .
We prove the quantum version - for Hecke algebras HAn of typeA at roots of unity - of Kleshchev's modular branching rulefor symmetric groups. This result describes the socle of therestriction of an irreducible HAn-module to the subalgebraHAn1. As a consequence, we describe the quantum versionof the Mullineux involution describing the irreducible moduleobtained on twisting an irreducible module with the sign representation.1991 Mathematics Subject Classification: 20C05, 20G05. 相似文献
In this paper we prove that the braid group Bn(S2) of 2-sphere, mapping class group M(0,n) of the n-punctured 2-sphere and the braid group B3(P2) of the projective plane are linear.
Partially supported by the Russian Foundation for Basic Research (grant number 02-01-01118).Mathematics Subject Classifications (2000) 20F28, 20F36, 20G35. 相似文献
When multidimensional scaling of n cases is derived from dissimilarities that are functions of p basic continuous variables, the question arises of how to relate the values of the variables to the configuration of n points. We provide a methodology based on nonlinear biplots that expresses nonlinearity in two ways: (i) each variable is represented by a nonlinear trajectory and (ii) each trajectory is calibrated by an irregular scale. Methods for computing, calibrating and interpreting these trajectories are given and exemplified. Not only are the tools of immediate practical utility but the methodology established assists in a critical appraisal of the consequences of using nonlinear measures in a variety of multidimensional scaling methods. 相似文献
We study properties of Jordan representations ofH-dissipative operators in a finite-dimensional indefiniteH-space. An algebraic proof is given of the fact that such operators always have maximal semidefinite invariant subspaces.
Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 163–169, February, 1998.
The authors axe grateful to Professor A. A. Shkalikov for useful discussions.
The research of the first author was supported by INTAS under grant No. 93-0249. The research of the second author was supported
by the International Science Foundation and the Russian Government under grant No. NZP300. 相似文献
We consider two-dimensional relativistically invariant systems with a three-dimensional reducible configuration space and
a chiral-type Lagrangian that admit higher symmetries given by polynomials in derivatives up to the fifth order. Nine such
systems are known: two are Liouville-type systems, and zero-curvature representations for two others have previously been
found. We here give zero-curvature representations for the remaining five systems. We show how infinite series of conservation
laws can be derived from the established zero-curvature representations. We give the simplest higher symmetries; others can
be constructed from the conserved densities using the Hamiltonian operator. We find scalar formulations of the spectral problems.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 189–205, August, 2006. 相似文献
We extend the Lévy inversion formula for the recovery of a bounded measure over from its Fourier-Stieltjes transform to bounded complex-valued, orthogonally scattered Hilbert space-valued, and spectral projection operator-valued measures over any first countable locally compact Abelian group. All our results are direct generalizations of known inversions for . 相似文献