On a Class of KMS States for the Unitary Group U (oo).
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Serban Stratila, Dan Voiculescu (1978)
Mathematische Annalen
Karl-H. Neeb (2011)
Annales de l’institut Fourier
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...
Henryk Hecht (1979)
Mathematische Annalen
J. Mickelsson, J. Niederle (1973)
Annales de l'I.H.P. Physique théorique
Henryk Hecht, Wilfried Schmid (1976)
Mathematische Annalen
Siddhartha Sahi (1989)
Compositio Mathematica
J.F. Price (1975)
Monatshefte für Mathematik
Nahlus, Nazih (2002)
Journal of Lie Theory
Sergey Oblezin (2012)
Open Mathematics
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...
Pascal Auscher, A. ter Elst, Derek Robinson (1994)
Colloquium Mathematicae
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...
Zoltán Magyar (1989)
Mathematica Scandinavica
Henryk Hecht, Wilfried Schmid (1983)
Journal für die reine und angewandte Mathematik
Winfried Schmid (1975)
Inventiones mathematicae
C. Cishahayo, S. De Bièvre (1993)
Annales de l'institut Fourier
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 .
Fujiwara, Hidenori (1997)
Journal of Lie Theory
Nolan R. Wallach (1976)
Annales scientifiques de l'École Normale Supérieure
Pawel Traczyk (1978)
Mathematische Zeitschrift
Andrzej Daszkiewicz, Tomasz Przebinda (1996)
Colloquium Mathematicae
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...
M. Kashiwara, M. Vergne (1978)
Inventiones mathematicae
Koichi Takase (1992)
Journal für die reine und angewandte Mathematik
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