By Daniel Canarutto, Arkadiusz Jadczyk, Marco Modugno (auth.), J.-P. Antoine, S. Twareque Ali, W. Lisiecki, I. M. Mladenov, A. Odzijewicz (eds.)

The XIIIth Bialowieza summer season Workshop was once held from July nine to fifteen, 1994. whereas nonetheless in the basic framework of Differential Geometric tools in Physics, the XnIth Workshop was once extended in scope to incorporate quantum teams, q-deformations and non-commutative geometry. it's anticipated that lectures on those themes will now turn into a vital part of destiny workshops. within the extra conventional components, lectures have been dedicated to subject matters in quantization, box concept, workforce representations, coherent states, complicated and Poisson buildings, the Berry part, graded contractions and a few infinite-dimensional platforms. these people who've taken half within the evolution of the workshops through the years, consider a great degree of pride with the wonderful caliber of the papers provided, specifically the mathematical rigour and novelty. every year an important variety of new effects are offered and destiny instructions of study are mentioned. Their freshness and immediacy necessarily ends up in excessive discussions and an alternate of rules in an off-the-cuff and bodily fascinating surroundings. the current workshop additionally had the next attendance than its predecessors, with ap­ proximately sixty five registered members. As traditional, there has been a lot of graduate scholars and younger researchers between them.

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Math. Phys. 33:6237-6243 (1994) 25. A. M. El Gradechi and S. De Bievre, Phase space quantum mechanics on the Anti-de Sitter spacetime and its Poincare contraction, Ann. Phys. (NY) 235:1-35 (1994) 26. A. W. Knapp, "Representation Theory of Semisimple Lie Groups", Princeton University Press, Princeton (1986) 27. M. Duflo and C. C. Moore, On the regular representation of a nonunimodular locally compact group, J. Funct. Analysis 21:209-243 (1976) 28. A. Grossmann, J. Morlet and T. Paul, Transforms associated to square integrable group representations.

N) is the braid group EN. An element ;Y of the universal covering space iiN can be labeled by a configuration /, together with a braid bEEN that specifies the sheet in iiN to which the element belongs; we shall write ;Y = (" b). This labeling is not unique, but conventional; the sheet associated with the identity element e E EN may be selected arbitrarily. We denote by p the projection mapping, p(;Y) = /. The braid group also acts on iiN; for b' E EN, we have b'( / , b) = (/, bb'). An equivariant wave function lj, is a complex-valued function on iiN that transforms in accordance with a char~ter T of EN; that is, lj,("bb') = T(b')lj,(" b).

E. 5). 3. GEOMETRIC QUANTIZATION FOR THE CCR The purpose of this section is to show how modular structures enter when the geometric quantization programme is applied to the canonical commutation relations. The first step is to choose the group on which this progamme will be carried out in the two steps below: prequantization and quantization. e. ), we had shown 21 how to control the classical limit of the quantum systems of imprimitivity based on these manifolds. 6) of Hf by IRn . \ t--+ 0 ): H~ = {a= (a\a2, ..

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