Harmonic analysis and the global exponential map for compact Lie groups

Dooley, A. H.; Wildberger, N. J.

doi:10.1007/bf01768664

Cited by 23 publications

(37 citation statements)

References 7 publications

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“…, λ n } be the fundamental dominant weights, i.e., the dual basis vectors which satisfy (α i , λ j ) = δ i j . 3 Given a set of l integers i 1 , . .…”

Section: Criterion For Belonging To Lmentioning

confidence: 99%

“…Given any compact Lie group G, we let be the wrapping map of G introduced by Dooley and Wildberger in [3], our main reference for this section. This is the map : M(g) → M(G) given by…”

Section: Transference Theoremmentioning

confidence: 99%

“…To obtain results about orbital measures supported on adjoint orbits in the algebra from these results for orbital measures on the group we prove a general transference theorem that is based on ideas of Dooley and Wildberger [3]. This can be found in Sect.…”

mentioning

confidence: 99%

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L 2-singular dichotomy for orbital measures of classical simple Lie algebras

2008

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“…, λ n } be the fundamental dominant weights, i.e., the dual basis vectors which satisfy (α i , λ j ) = δ i j . 3 Given a set of l integers i 1 , . .…”

Section: Criterion For Belonging To Lmentioning

confidence: 99%

“…Given any compact Lie group G, we let be the wrapping map of G introduced by Dooley and Wildberger in [3], our main reference for this section. This is the map : M(g) → M(G) given by…”

Section: Transference Theoremmentioning

confidence: 99%

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L 2-singular dichotomy for orbital measures of classical simple Lie algebras

2008

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“…We may compare this expression with a calculation in [9]. According to the formula there on the bottom of p. 22, for any function φ on h/H ,…”

Section: Stacks Of Conjugacy Classes and Adjoint Orbitsmentioning

confidence: 98%

The Volume of a Differentiable Stack

Weinstein

2009

Lett Math Phys

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Abstract. We extend the notion of the cardinality of a discrete groupoid (equal to the Euler characteristic of the corresponding discrete orbifold) to the setting of Lie groupoids. Since this quantity is an invariant under equivalence of groupoids, we call it the volume of the associated stack rather than of the groupoid itself. Since there is no natural measure in the smooth case like the counting measure in the discrete case, we need extra data to define the volume. This data has the form of an invariant section of a natural line bundle over the base of the groupoid. Invariant sections of a square root of this line bundle constitute an "intrinsic Hilbert space" of the stack. Mathematics Subject Classification (2000). Primary 58H05; Secondary 53D17.

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“…We will use notation from [3] and [4]; this is almost standard for compact Lie groups, but let us recall some of the more important definitions, normalizations, etc.…”

Section: Modulatorsmentioning

confidence: 99%