This quantity includes the court cases of the convention on illustration concept 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 primary function of arithmetic, particularly as a result of connections to geometry, topology, quantity thought, physics, combinatorics, and plenty of different parts. illustration thought is likely one of the cornerstones of the Langlands application in quantity conception, courting to the Seventies. Zuckerman's paintings on derived functors, the interpretation precept, and coherent continuation lie on the middle of the trendy concept of representations of Lie teams. one of many significant unsolved difficulties in illustration thought is that of the unitary twin. the truth that there's, in precept, a finite set of rules for computing the unitary twin is based seriously on Zuckerman's paintings. lately there was a fruitful interaction among arithmetic and physics, in geometric illustration thought, string thought, and different parts. New advancements on chiral algebras, illustration concept of affine Kac-Moody algebras, and the geometric Langlands correspondence are the various focal issues of this quantity. contemporary advancements within the geometric Langlands application aspect to intriguing connections among definite automorphic representations and twin fibrations in geometric replicate symmetry.
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