This quantity includes the complaints of the convention on illustration conception and Mathematical Physics, in honor of Gregg Zuckerman's sixtieth birthday, held October 24-27, 2009, at Yale college. Lie teams and their representations play a basic function of arithmetic, particularly due to connections to geometry, topology, quantity thought, physics, combinatorics, and plenty of different components. illustration conception is likely one of the cornerstones of the Langlands application in quantity concept, relationship to the Seventies. Zuckerman's paintings on derived functors, the interpretation precept, and coherent continuation lie on the middle of the fashionable conception of representations of Lie teams. one of many significant unsolved difficulties in illustration concept is that of the unitary twin. the truth that there's, in precept, a finite set of rules for computing the unitary twin is predicated seriously on Zuckerman's paintings. in recent times there was a fruitful interaction among arithmetic and physics, in geometric illustration conception, string thought, and different parts. New advancements on chiral algebras, illustration thought of affine Kac-Moody algebras, and the geometric Langlands correspondence are many of the focal issues of this quantity. fresh advancements within the geometric Langlands software aspect to intriguing connections among yes automorphic representations and twin fibrations in geometric replicate symmetry.

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