Results 301 to 310 of about 872,521 (356)

A proof of the polynomial conjecture for restrictions of nilpotent lie groups representations

Representation Theory of the American Mathematical Society, 2022
Let G G be a connected and simply connected nilpotent Lie group, K K an analytic subgroup of G G and π \pi an irreducible unitary representation of G G whose coadjoint orbit of G G is denoted by Ω ( π ) \
Baklouti, Ali, Fujiwara, Hidenori, Ludwig, Jean   +2 more
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A homotopy construction of the adjoint representation for Lie groups

Mathematical Proceedings of the Cambridge Philosophical Society, 2002
Let G be a compact, simply-connected, simple Lie group and T ⊂ G a maximal torus. The purpose of this paper is to study the connection between various fibrations over BG (where G is a compact, simply-connected, simple Lie group) associated to the adjoint representation and homotopy colimits over poset categories [Cscr ], hocolim[Cscr ]BGI where
Castellana, Natàlia, Kitchloo, Nitu
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Representations of differential operators on a Lie group, and conditions for a Lie algebra of operators to generate a representation of the group

Journal d'Analyse Mathématique, 1983
Let G be a simply connected Lie group with Lie algebra \({\mathcal G}\). If U is a unitary representation of G then let dU denote the corresponding infinitesimal representation of \({\mathcal G}\). Now suppose that \(\rho\) is any densely defined representation of the Lie algebra. There are two problems considered in this paper.
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A note on coherent state representations of Lie groups

Journal of Mathematical Physics, 1975
The analyticity properties of coherent states for a semisimple Lie group are discussed. It is shown that they lead naturally to a classical ’’phase space realization’’ of the group.
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Reduction theory for stably graded Lie algebras

Algebra & Number Theory
We define a reduction covariant for the representations a la Vinberg associated to stably graded Lie algebras. We then give an analogue of the LLL algorithm for the odd split special orthogonal group and show how this can be combined with our theory to ...
Jack A. Thorne
semanticscholar   +1 more source

A geometric construction of local representations of local Lie groups

Acta Applicandae Mathematicae, 1991
Let \(S\) be a local Lie subgroup of a Lie group \(G\) with an involutive automorphism \(\sigma\) of \(G\) such that \(\sigma(S)=S\). Suppose that \(S\) acts as a local transformation group on a manifold \(X\). One defines a local multiplier action, \(\tau(g)f(x)=m(x,g)f(g^{-1}x)\), of \(S\) on the space \({\mathcal D}(X)\) of \(C^ \infty\) functions ...
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A Garding domain for representations of some Hilbert Lie groups

Letters in Mathematical Physics, 1975
Given a Banach representation of a Hilbert Lie group, the Lie algebra $$\mathfrak{G}$$ of which is the closure of the union of an increasing sequence of finite dimensional subalgebras, we construct a Garding domain on which we differentiate the group ...
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A reciprocity theorem for unitary representations of Lie groups

Israel Journal of Mathematics, 1973
LetG be a Lie group,H a closed subgroup,L a unitary representation ofH andU L the corresponding induced representation onG. The main result of this paper, extending Ol’ŝanskii’s version of the Frobenius reciprocity theorem, expresses the intertwining number ofU L and an irreducible unitary representationV ofG in terms ofL and the restriction ofV ∞ toH.
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Finite Dimensional Representations of a Semi-Simple Lie Group

1972
Let G be a connected semi-simple Lie group with finite center, say — then it is not necessarily the case that G possesses enough finite dimensional representations to separate points (cf. 3.1.1). In fact G will, in general, admit no non-trivial finite dimensional unitary representations (cf. number 4.3.2).
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The Left-Regular Representation of a Super Lie Group

2019
With the usual definition of a super Hilbert space and a super unitary representation, it is easy to show that there are lots of super Lie groups for which the left-regular representation is not super unitary. I will show that weakening the definition of a super Hilbert space (by allowing the super scalar product to be non-homogeneous, not just even ...
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