Displaying similar documents to “A Cauchy Problem for Elliptic Invariant Differential Operators and Continuity of a generalized Berezin transform”

Gelfand transforms of S O ( 3 ) -invariant Schwartz functions on the free group N 3 , 2

Véronique Fischer, Fulvio Ricci (2009)

Annales de l’institut Fourier

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The spectrum of a Gelfand pair ( K ⋉ N , K ) , where N is a nilpotent group, can be embedded in a Euclidean space. We prove that in general, the Schwartz functions on the spectrum are the Gelfand transforms of Schwartz K -invariant functions on N . We also show the converse in the case of the Gelfand pair ( S O ( 3 ) ⋉ N 3 , 2 , S O ( 3 ) ) , where N 3 , 2 is the free two-step nilpotent Lie group with three generators. This extends recent results for the Heisenberg group.

Rankin–Cohen brackets and representations of conformal Lie groups

Michael Pevzner (2012)

Annales mathématiques Blaise Pascal

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This is an extended version of a lecture given by the author at the summer school “Quasimodular forms and applications” held in Besse in June 2010. The main purpose of this work is to present Rankin-Cohen brackets through the theory of unitary representations of conformal Lie groups and explain recent results on their analogues for Lie groups of higher rank. Various identities verified by such covariant bi-differential operators will be explained by the associativity of a...

Conformally invariant trilinear forms on the sphere

Jean-Louis Clerc, Bent Ørsted (2011)

Annales de l’institut Fourier

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To each complex number λ is associated a representation π λ of the conformal group S O 0 ( 1 , n ) on 𝒞 ∞ ( S n - 1 ) (spherical principal series). For three values λ 1 , λ 2 , λ 3 , we construct a trilinear form on 𝒞 ∞ ( S n - 1 ) × 𝒞 ∞ ( S n - 1 ) × 𝒞 ∞ ( S n - 1 ) , which is invariant by π λ 1 ⊗ π λ 2 ⊗ π λ 3 . The trilinear form, first defined for ( λ 1 , λ 2 , λ 3 ) in an open set of ℂ 3 is extended meromorphically, with simple poles located in an explicit family of hyperplanes. For generic values of the parameters, we prove uniqueness of trilinear invariant forms.

Constant term in Harish-Chandra’s limit formula

Mladen Božičević (2008)

Annales mathématiques Blaise Pascal

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Let G ℝ be a real form of a complex semisimple Lie group G . Recall that Rossmann defined a Weyl group action on Lagrangian cycles supported on the conormal bundle of the flag variety of G . We compute the signed average of the Weyl group action on the characteristic cycle of the standard sheaf associated to an open G ℝ -orbit on the flag variety. This result is applied to find the value of the constant term in Harish-Chandra’s limit formula for the delta function at zero.

Is the Luna stratification intrinsic?

Jochen Kuttler, Zinovy Reichstein (2008)

Annales de l’institut Fourier

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Let G → GL ( V ) be a representation of a reductive linear algebraic group G on a finite-dimensional vector space V , defined over an algebraically closed field of characteristic zero. The categorical quotient X = V // G carries a natural stratification, due to D. Luna. This paper addresses the following questions: (i) Is the Luna stratification of X intrinsic? That is, does every automorphism of V // G map each stratum to another stratum? (ii) Are the individual Luna strata in X intrinsic?...