منابع مشابه
Combinatorics and invariant differential operators on multiplicity free spaces
where Λ+ is a set of dominant weights and Mλ is a simple G-module of lowest weight −λ. All elements of Mλ are homogeneous of the same degree, denoted l(λ). Now consider an invariant differential operator D on U . It will act on each irreducible constituent Mλ as a scalar, denoted by cD(λ). It can be shown that cD extends to a polynomial function to V , the C-span of Λ+. Thus, D 7→ cD is a homom...
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Abstract. In a recent paper, the authors have constructed a large class of operators in the Cowen-Douglas class Cowen-Douglas class of the unit disc D which are homogeneous with respect to the action of the group Möb – the Möbius group consisting of bi-holomorphic automorphisms of the unit disc D. The associated representation for each of these operators is multiplicity free. Here we give a dif...
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The analysis of invariant differential operators on certain multiplicity free spaces led recently to the introduction of a family of symmetric polynomials that is more general than Jack polynomials (see [KS], but also [OO1], [OO2]). They are called interpolation Jack polynomials, shifted Jack polynomials, or Capelli polynomials. Apart from being inhomogeneous, they are distinguished from classi...
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We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schrödinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the interior vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of ...
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Abstract. We extend our earlier work in [TZ1], where an analytic approach to the GuilleminSternberg conjecture [GS] was developed, to cases where the Spin-complex under consideration is allowed to be further twisted by certain exterior power bundles of the cotangent bundle. The main result is a weighted quantization formula in the presence of commuting Hamiltonian actions. The corresponding Mor...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2015
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-015-1247-8