منابع مشابه
Some remarks on multiplicity free spaces
We study multiplicity free representations of connected reductive groups. First we give a simple criterion to decide the multiplicity freeness of a representation. Then we determine all invariant differential operators in terms of a finite reflection group, the little Weyl group, and give a characterization of the spectrum of the Capelli operators. At the end, we reproduce the classification of...
متن کاملCombinatorics 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...
متن کاملInfinite Dimensional Multiplicity Free Spaces II: Limits of Commutative Nilmanifolds
We study direct limits (G,K) = lim −→ (Gn, Kn) of Gelfand pairs of the form Gn = Nn Kn with Nn nilpotent, in other words pairs (Gn, Kn) for which Gn/Kn is a commutative nilmanifold. First, we extend the criterion of [W4] for a direct limit representation to be multiplicity free. Then we study direct limits G/K = lim −→ Gn/Kn of commutative nilmanifolds and look to see when the regular represent...
متن کاملConstruction of Commuting Difference Operators for Multiplicity Free Spaces
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...
متن کاملMultiplicity of Mental Spaces
When asked the direction between Phildadelphia and Rome, most people err. They say that Philadelphia is north of Rome when in fact, it is south of Rome. This cannot be dismissed as the weather, because when asked the direction between Boston and Rio, a majority of people erroneously say that Boston is east of Rio. Nor are these errors a simple consequence of randomness, nor of ignorance of geog...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1984
ISSN: 0022-040X
DOI: 10.4310/jdg/1214438422