On a Class of KMS States for the Unitary Group U (oo).
On Analytic Vectors for Unitary Representations of Infinite Dimensional Lie Groups
Let be a connected and simply connected Banach–Lie group. On the complex enveloping algebra of its Lie algebra we define the concept of an analytic functional and show that every positive analytic functional is integrable in the sense that it is of the form for an analytic vector of a unitary representation of . On the way to this result we derive criteria for the integrability of -representations of infinite dimensional Lie algebras of unbounded operators to unitary group representations.For...
On Characters and Asymptotics of Representations of a Real Reductive Lie Group.
On integrability of discrete representations of Lie algebra
On Integrable Representations of a Semisimple Lie Group.
On Kirillov's conjecture for archimedean fields
On Local Central Lacunary Sets for Compact Lie Groups.
On observable subgroups of complex analytic groups and algebraic structures on analytic homogeneous spaces.
On parabolic Whittaker functions II
We propose a Givental-type stationary phase integral representation for the restricted Grm,N-Whittaker function, which is expected to describe the (S 1×U N)-equivariant Gromov-Witten invariants of the Grassmann variety Grm,N. Our key tool is a generalization of the Whittaker model for principal series U(gl N)-modules, and its realization in the space of functions of totally positive unipotent matrices. In particular, our construction involves a representation theoretic derivation of the Batyrev-Ciocan-Fontanine-Kim-van...
On positive Rockland operators
Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on . Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on we prove that it is closed on each of the -spaces, p ∈ 〈 1,∞〉, and that it generates a semigroup S with a smooth kernel K which, with its derivatives, satisfies Gaussian bounds. The semigroup is holomorphic in the open right half-plane on all the -spaces, p ∈ [1,∞]. Further extensions...
On the analytic vector variant of the Hille-Yosida theorem.
On the asymptotics of Harish-Chandra modules.
On the Characters of the Directe Series. The Hermitian Symmetric Case.
On the contraction of the discrete series of
It is shown, using techniques inspired by the method of orbits, that each non-zero mass, positive energy representation of the Poincaré group can be obtained via contraction from the discrete series of representations of .
On the Corwin-Greenleaf conjecture. (Sur la conjecture de Corwin-Greenleaf.)
On the Enright-Varadarajan modules : a construction of the discrete series
On the G-Homotopy Equivalence of Spheres of Representations.
On the Moment Map of a Multiplicity Free Action
The purpose of this note is to show that the Orbit Conjecture of C. Benson, J. Jenkins, R. L. Lipsman and G. Ratcliff [BJLR1] is true. Another proof of that fact has been given by those authors in [BJLR2]. Their proof is based on their earlier results, announced together with the conjecture in [BJLR1]. We follow another path: using a geometric quantization result of Guillemin-Sternberg [G-S] we reduce the conjecture to a similar statement for a projective space, which is a special case of a characterization...
On the Segal-Shale-Weil Representations and Harmonic Polynomials.
On unitary representations of Jacobi groups.