By Pavel Etingof, Shlomo Gelaki, Steven Shnider

The papers during this quantity are according to the talks given on the convention on quantum teams devoted to the reminiscence of Joseph Donin, which used to be held on the Technion Institute, Haifa, Israel in July 2004. A survey of Donin's amazing mathematical profession is integrated. numerous articles, that have been at once encouraged by way of the examine of Donin and his colleagues, care for invariant quantization, dynamical $R$-matrices, Poisson homogeneous areas, and mirrored image equation algebras. the subjects of alternative articles comprise Hecke symmetries, orbifolds, set-theoretic recommendations to the pentagon equations, representations of quantum present algebras, unipotent crystals, the Springer answer, the Fourier rework on Hopf algebras, and, as a transformation of speed, the combinatorics of easily knotted surfaces. The articles all comprise very important new contributions to their respective parts and may be of significant curiosity to graduate scholars and study mathematicians attracted to Hopf algebras, quantum teams, and purposes. info for our vendors: This e-book is copublished with Bar-Ilan college (Ramat-Gan, Israel)

**Read Online or Download Quantum Groups: Israel Mathematical Conference Proceedings, Proceedings of a Conference in Memory of Joseph Donin, July 5-12, 2004, Technion-israel Institute of Techn PDF**

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**Additional info for Quantum Groups: Israel Mathematical Conference Proceedings, Proceedings of a Conference in Memory of Joseph Donin, July 5-12, 2004, Technion-israel Institute of Techn**

**Example text**

In particular. it E 12(Z~) of arbitrarily small norm may be chosen such that. with v - I(jl)-' a; Jf. Ov-O. vl/_o -80' d1vl/_0 - 8,. 8,) - (O). I;Bp,·v 3 1! H3s-n~2~"(Itn~') for any j. 8). If (Ilk) is a collection of seminorms on M. define C;,k,J1I - (fJ E M: III;A(fJ)IIu3s-n+2+c ~ mlfJlk)' It is easily seen that Cj,k,J1I is closed in M. 8), ~ f! C;,k,J1I' and therefore q,k,J1I is nowhere dense in M. 9) I;BfJv3 f! H3s-n+2+t(Rn+l)for any j. 1 1x Rn). 9) that Ou-fJu 3, « that is, u is singular on the truncated solid light cone I,I): III S I, 0 S I ~ I).

F). (Since the nonlinear function depends only on u and not on Ou, microlocal regularity is propagated up to order r < 2 s - (n. ) By the algebra property. A F). /( F). 1 0 and its eItension to functions of differing regularities that to '" II. 0. Eli H26+512+2rm,(f). 3), u i H26+512+2tJJ1Af) as long as r < 114. In particular, the singular support of u contains the forward characteristic (x - 0, t ) OJ. 2. 1. let jJ E coo(12), fJ '"' O. I ~ -112. fJ .. 1, t 2 O. For 80y s > 1 there is a choice of Cauchy data (go.

AInu), then the chain rule and the expressions for the commutators imply that there are smooth vector valued functions g and h and there is a smooth vector valued differential operator rill -I( I,I,O) such that Pill ( I,I,J)){! - g( I,I,U, ... ,j)IIl-1 u) + rlll_IU,I,j))lf. By assumption, if k l 1. [! E HS/««(t < 0)). Schauder's Lemma and the linear energy inequality then imply that [! r). 2 used in place of Schauder's Lemma. D. Now suppose that a solution is known to be conormal in the past with respect to a pair of characteristic hypersurfaces which intersect transversally in the future.