Workshop on Hecke Algebras and Lie Theory

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This award supports US-based participants, primarily graduate students and postdoctoral researchers, in the "Workshop on Hecke Algebras and Lie Theory," held May 12-15, 2016 at the University of Ottawa. The workshop brings together experts in algebraic combinatorics and Lie theory with the goal of fostering the international collaboration between researchers in several areas connected to representation theory and algebraic combinatorics, including Lie superalgebras, extended affine Lie algebras, and Hecke algebras. In addition to talks by experts in the field, the workshop includes a mini-course accessible to non-experts, including junior researchers, that covers recent progress in double affine Hecke algebras and related areas. Hecke algebras of finite and affine Weyl groups arise naturally as convolution algebras associated to finite and locally compact groups, and they play a prominent role in the representation theory of finite groups of Lie type and of reductive p-adic groups. In the early 1990's a class of algebras, known as double affine Hecke algebras, was introduced in connection with affine quantum Knizhnik-Zamolodchikov equations. Since then, profound connections have been discovered between double affine Hecke algebras and a broad spectrum of areas in mathematics, including combinatorics, algebraic geometry, number theory, representation theory, harmonic analysis, knot theory, special functions, many body problems, and conformal field theory. Recent results hint at a new and promising connection between double affine Hecke algebras and Lie superalgebras and open the door to many intriguing possibilities that will be explored at the workshop. The website for the workshop is https://www.fields.utoronto.ca/programs/scientific/15-16/Hecke/