Algebraic Lie Theory

by Cambridge University

Lie theory has profound connections to many areas of pure and applied mathematics and mathematical physics. In the 1950s, the original "analytic" theory was extended so that it also makes sense over arbitrary algebraically closed fields, in particular, fields of positive characteristic. Understanding fundamental objects such as Lie algebras, quantum groups, reductive groups over finite or p-adic fields and Hecke algebras of various kinds, as well as their representation theory, are the central themes of "Algebraic Lie Theory".A driving force has always been the abundance of challenging, yet very basic problems, like finding explicit character formulae for representations. The introduction of geometric methods (in the 1970s) has revolutionized the field. It led to a flow of new ideas between several disciplines, and produced spectacular advances. The ideas of "geometrization" and "categorification" now play a fundamental role in the development of the subject. New structures continue to arise from connections with other areas of mathematics and mathematical physics, like the emerging theory of W-algebras.Read more at: www.newton.ac.uk/programmes/ALT/

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Recent Episodes
  • Arithmetic cycles on moduli spaces of abelian varieties
    Apr 20, 2011 – 01:01:03
  • L-functions and arithmetic
    Apr 20, 2011 – 01:02:26
  • What is an algebraic automorphic form?
    Apr 20, 2011 – 01:08:12
  • Affine Gelfand-Tsetlin bases and affine Laumon spaces
    May 24, 2011 – 01:02:38
  • Affine W-algebras and Zhu's Poisson varieties associated with Kac-Moody vertex algebras
    May 23, 2011 – 58:01
  • Algebraic group analogues of the Slodowy slices and deformed Poisson W-algebras
    May 23, 2011 – 01:08:01
  • Algeraic Lie Theory through the Symmetric Group
    Jun 24, 2009 – 56:28
  • An action of SL(2,Z) on the space of Dirichlet series, and some associated computations
    Apr 20, 2011 – 01:03:24
  • An algebraic slice in the coadjoint action of the Borel
    May 27, 2011 – 01:02:59
  • An explicit construction of the complex of variational calculus and Lie conformal algebra cohomology
    May 24, 2011 – 01:04:17
  • Atypicality, complexity and module varieties for classical Lie superalgebras
    Jun 1, 2011 – 56:40
  • Blocks and decomposition numbers for the Brauer algebra
    May 20, 2011 – 01:04:04
  • Blocks of the general linear supergroup
    May 31, 2011 – 01:10:43
  • Braid groups and representations of symmetric groups
    May 27, 2011 – 01:08:27
  • Brauer height zero conjecture for 2-blocks of maximal defect
    Apr 20, 2011 – 01:04:00
  • Canonical bases and KLR-algebras
    Jun 1, 2011 – 01:02:42
  • Carter-Payne homomorphisms for Hecke algebras
    Jun 24, 2009 – 01:00:26
  • Categorification and finite dimensional modules of DAHA
    Sep 19, 2011 – 59:11
  • Categorification of sl(2)-modules 1
    May 18, 2011 – 01:03:33
  • Categorification of sl(2)-modules 2
    May 19, 2011 – 01:01:34
  • Categorification of sl(2)-modules 3
    May 19, 2011 – 01:02:03
  • Categorification, canonical bases and knot invariants
    Sep 19, 2011 – 01:06:25
  • CFSG and group theory
    May 27, 2011 – 01:02:26
  • Cherednik algebra, Calogero-Moser space and Bethe ansatz
    May 23, 2011 – 01:00:56
  • Chiral differential operators on flag manifolds and Kac-Moody algebras at the critical level
    Jul 2, 2009 – 53:43
  • Cluster algebras via quivers with potentials
    May 26, 2011 – 59:27
  • Cohomology of the minimal nilpotent orbit
    May 25, 2011 – 01:01:36
  • Combinatorics of Kazhdan-Lusztig cells
    May 20, 2011 – 01:09:30
  • Compactification of Deligne-Lusztig varieties
    Jun 2, 2011 – 01:07:36
  • Complete reducibility and rationality
    May 20, 2011 – 57:31
  • Complex reflection groups and their associated braid groups and Hecke algebras 1
    May 19, 2011 – 58:29
  • Complex reflection groups and their associated braid groups and Hecke algebras 2
    May 19, 2011 – 01:01:23
  • Complex reflection groups and their associated braid groups and Hecke algebras 3
    May 19, 2011 – 55:56
  • Conformal field theory and Cherednik algebras
    May 23, 2011 – 01:02:16
  • Convolution algebras: an explicit construction
    May 20, 2011 – 01:04:20
  • Crystal structure for representations of Cherednik algebras
    May 23, 2011 – 01:08:55
  • Decomposition matrices and parametrisations of simple modules for Hecke algebras
    May 25, 2011 – 59:43
  • Deligne-Lusztig varieties and cyclotomic Hecke algebras
    May 25, 2011 – 01:14:26
  • Deligne-Lusztig varieties, Braid groups and cyclotomic Hecke algebras
    Jun 2, 2011 – 01:03:04
  • Density of character degrees
    May 31, 2011 – 57:47
  • Derangements in Finite and Algebraic Groups
    Jun 1, 2011 – 59:34
  • Derived categories and perverse sheaves 1
    May 18, 2011 – 01:03:29
  • Derived categories and perverse sheaves 2
    May 18, 2011 – 59:32
  • Derived categories and perverse sheaves 3
    May 19, 2011 – 49:39
  • Derived categories and perverse sheaves 4
    May 19, 2011 – 58:56
  • Derived categories and perverse sheaves 5
    May 19, 2011 – 53:42
  • Difference spherical and Whittaker functions
    Jun 1, 2011 – 01:07:10
  • Differential operators on quantized flag manifolds
    Sep 19, 2011 – 52:52
  • Double Cells and Representations
    Sep 19, 2011 – 59:01
  • Dunkl operators for symplectic reflection algebras of wreath-product types
    May 23, 2011 – 01:00:38
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