Lie Groups, Geometry, and Representation Theory

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This volume honors the memory of the esteemed American mathematician Bertram Kostant and contains 19 invited papers from leading experts in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant's groundbreaking contributions have significantly advanced these fields, fostering new insights and research areas. The collection includes the only published articles detailing recent important results from the contributors, complete with proofs. Key topics addressed in the volume encompass Poisson structures and potentials, vertex algebras, modular irreducible representations of semisimple Lie algebras, and asymptotic Hecke algebras. Additional discussions cover tensor categories and quantum groups, nil-Hecke algebras and Whittaker D-modules, Toeplitz operators, Kashiwara crystals, and characters of highest weight modules. The volume also explores alcove polytopes, representation theory of quantized Gieseker varieties, generalized Bruhat cells and integrable systems, almost characters, Verlinde formulas, the Dirac operator and equivariant index, modality of representations, and the geometry of θ-groups, as well as distributions on homogeneous spaces and the reduction of orthogonal representations. This rich compilation reflects the depth and breadth of contemporary mathematical research inspired by Kostant's legacy.