Algebraic Lie theory

Programme theme

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.

It is anticipated that the activities of the programme will lead to a focalisation and popularisation of the various recent methods, advances and applications of Algebraic Lie Theory.

The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:

The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Algebraic Lie theory, where work on this paper was undertaken. This work was supported by EPSRC grant EP/F005431/1.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme	Publication Date
Closed orbits and uniform $\it S$-instability in invariant theory Authors: Michael Bate, Benjamin Martin, Gerhard Röhrle, Rudolf Tange Download PDF	2008	ALT	21 October 2016
Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras Authors: Michael Bate, Benjamin Martin, Gerhard Röhrle, Rudolf Tange Download PDF	2008	ALT	21 October 2016
On 1-dimensional representations of finite $\it W$-algebras associated to simple Lie algebras of exceptional type Authors: Simon Goodwin, Gerhard Röhrle, Glenn Ubly Download PDF	2008	ALT	21 October 2016
Highest weight categories arising from Khovanov's diagram algebra II: Koszulity Authors: Jon Brundan, Catharina Stroppel Download PDF	2008	ALT	21 October 2016
Highest weight categories arising from Khovanov's diagram algebra III: Category $\mathcal O$ Authors: Catharina Stroppel, Jon Brundan Download PDF	2008	ALT	21 October 2016
Highest weight categories arising from Khovanov's diagram algebra IV: The general linear supergroup Authors: Catharina Stroppel, Jon Brundan Download PDF	2008	ALT	21 October 2016

Workshops

ALTW01

Instructional workshop

12 January 2009 to 23 January 2009

ALTW02

Algebraic Lie structures with origins in physics

23 March 2009 to 27 March 2009

Satellite

ALTW03

Seminars

Tuesday 5th February 2008
15:00 to 16:00	Stuart Martin University of Cambridge Complete reducibility and rationality	Room 1

Tuesday 27th January 2009
15:00 to 16:00	Anton Gawain Cox City University, London Blocks and decomposition numbers for the Brauer algebra	Room 1

Thursday 29th January 2009
15:00 to 16:00	Finite groups, black box groups, algebraic groups	Room 1

Thursday 5th February 2009
15:00 to 16:00	Stuart Martin University of Cambridge Complete reducibility and rationality	Room 1

Tuesday 10th February 2009
15:00 to 16:00	Michael Bate University of York Tits' centre conjecture for subgroups of algebraic groups	Room 1

Thursday 12th February 2009
15:00 to 16:00	Lacrimioara Iancu University of Aberdeen Combinatorics of Kazhdan-Lusztig cells	Room 1

Tuesday 17th February 2009
14:00 to 15:00	Steen Ryom-Hansen Universidad de Talca On the denominators of Young's seminormal basis	Room 1
15:15 to 16:15	Ken Brown University of Glasgow Hopf algebras of small Gelfand-Kirillov dimension	Room 1

Thursday 19th February 2009
15:00 to 16:00	David Hernandez CNRS - Ecole Normale Superieure Paris G-bundles on elliptic curves and quantum groups	Room 1

Tuesday 24th February 2009
15:00 to 16:00	Friedrich Knop Friedrich-Alexander-Universität Erlangen-Nürnberg On the representation of St when t is not a natural number	Room 1

Thursday 26th February 2009
10:00 to 11:00	Nilpotent subalgebras of semisimple Lie algebras, some unexpected torsion	Room 1
11:15 to 12:15	Gary Seitz University of Oregon Unipotent and nilpotent elements in simple algebraic groups	Room 1

Tuesday 3rd March 2009
14:00 to 15:00	Catharina Stroppel Rheinische Friedrich-Wilhelms-Universität Bonn Convolution algebras: an explicit construction	Room 1
15:15 to 16:15	Claus Michael Ringel Universität Bielefeld Root systems and canonical algebras	Room 1

Thursday 5th March 2009
15:00 to 16:00	Paul Levy Periodic automorphisms of semisimple Lie algebras	Room 1

Tuesday 10th March 2009
14:00 to 15:00	Alexander Ivanovich Molev University of Sydney Littlewood-Richardson polynomials	Room 1
15:15 to 16:15	Markus Perling Ruhr-Universität Bochum Exceptional sequences of invertible sheaves on rational surfaces	Room 1

Thursday 12th March 2009
15:00 to 16:00	Olivier Brunat Ruhr-Universität Bochum A basic set for the alternating group	Room 1

Tuesday 17th March 2009
14:00 to 15:00	Rolf Farnsteiner Bielefeld University Support spaces, Jordan types and indecomposable modules	Room 1
15:15 to 16:15	Gerhard Richard Hiss RWTH Aachen University The Weil-Steinberg character of finite classical groups	Room 1

Thursday 19th March 2009
15:00 to 16:00	Michel Duflo Université Paris 7 - Denis-Diderot Quasi-reductive Lie algebras	Room 1

Tuesday 31st March 2009
15:00 to 16:00	Jean Michel Université Paris 7 - Denis-Diderot Deligne-Lusztig varieties and cyclotomic Hecke algebras	Room 1

Thursday 2nd April 2009
14:00 to 15:00	Gunter Malle Technische Universität Kaiserslautern On the number of conjugacy classes of a finite group	Room 1
15:15 to 16:15	Simon Goodwin University of Birmingham Translations for finite W-algebras	Room 1

Tuesday 7th April 2009
15:00 to 16:00	Nicolas Jacon Université de Franche-Comté Decomposition matrices and parametrisations of simple modules for Hecke algebras	Room 1

Thursday 9th April 2009
15:00 to 16:00	Peter Fiebig Friedrich-Alexander-Universität Erlangen-Nürnberg Lusztig's conjecture via moment graphs	Room 1

Tuesday 21st April 2009
15:00 to 16:00	Tim Burness University of Southampton Permutation groups, derangements and prime order elements	Room 1

Thursday 23rd April 2009
14:00 to 15:00	J Matthew Douglass University of North Texas L-small representations of a reductive group	Room 1
15:15 to 16:15	Stephen Donkin University of York Some recent observations on generalised Schur algebras	Room 1

Tuesday 28th April 2009
14:00 to 15:00	Daniel Juteau CNRS - Université de Caen Basse-Normandie Cohomology of the minimal nilpotent orbit	Room 1
15:15 to 16:15	Marie-France Vigneras Université Paris 7 - Denis-Diderot Towards a p-adic Langlands correspondence: construction of (phi, Gamma)-modules	Room 1

Thursday 30th April 2009
14:00 to 15:00	Jeremie Guilhot University of Sydney Kazhdan-Lusztig cells in affine Weyl groups	Room 1
15:15 to 16:15	Joel Kamnitzer University of Toronto MV polytopes and components of quiver varieties	Room 1

Tuesday 5th May 2009
10:00 to 12:00	Laurent Lafforgue IHES Trying to construct explicitly kernels for Langlands' functoriality 1	Room 1
15:00 to 16:00	Emmanuel Letellier CNRS - Université de Caen Basse-Normandie Topology of quiver varieties and the character ring of finite general linear groups	Room 1

Thursday 7th May 2009
14:00 to 15:00	Geordie Williamson University of Oxford Some geometric constructions of link homology	Room 1
15:15 to 16:15	Goetz Pfeiffer National University of Ireland, Maynooth Quiver presentations of descent algebras of finite Coxeter groups	Room 1

Monday 11th May 2009
17:00 to 18:00	Laurent Lafforgue IHES RVP lecture: Langlands' functoriality viewed as a kind of function theoretic Poisson formula problem	Room 1

Tuesday 12th May 2009
10:00 to 12:00	Laurent Lafforgue IHES Trying to construct explicitly kernels for Langlands' functoriality 2	Room 1

Thursday 14th May 2009
14:00 to 15:00	Charlie Curtis University of Oregon Refinements of the Bruhat decomposition and structure constants of Hecke algebras of finite Chevally groups	Room 1
15:15 to 16:15	Andrei Zelevinsky Northeastern University Cluster algebras via quivers with potentials	Room 1

Tuesday 19th May 2009
10:00 to 12:00	Laurent Lafforgue IHES Trying to construct explicitly kernels for Langlands' functoriality 3	Room 1
15:15 to 16:15	Corrado De Concini Università degli Studi di Roma La Sapienza Quotients of symmetric varieties	Room 1
16:30 to 17:30	Claudio Procesi Università degli Studi di Roma La Sapienza From splines to the index theorem	Room 1

Thursday 21st May 2009
14:00 to 15:00	Types for p-adic classical groups	Room 1
15:15 to 16:15	Anthony Joseph University of California, Irvine and Weizmann Institute of Science An algebraic slice in the coadjoint action of the Borel	Room 1

Tuesday 26th May 2009
10:00 to 12:00	Laurent Lafforgue IHES Trying to construct explicitly kernels for Langlands' functoriality 4	Room 1
15:00 to 16:00	Eric Sommers University of Massachusetts Two partially ordered sets arising from nilpotent orbits	Room 1

Thursday 4th June 2009
14:00 to 15:00	Henning Haahr Andersen Aarhus Universitet Rigidity of tilting modules	Room 1
15:15 to 16:15	Alexander Braverman Brown University Quantum cohomology of the Springer resolution and affine KZ connections	Room 1

Tuesday 9th June 2009
15:00 to 16:00	Thomas Lam Harvard University Total positivity for loop groups	Room 1

Tuesday 16th June 2009
14:00 to 15:00	Anthony Henderson University of Sydney Geometry of the exotic nilpotent cone	Room 1
15:15 to 16:15	Andrew Mathas University of Sydney Carter-Payne homomorphisms for Hecke algebras	Room 1

Thursday 18th June 2009
15:00 to 16:00	Tomoyuki Arakawa Kyoto University Chiral differential operators on flag manifolds and Kac-Moody algebras at the critical level	Room 1

Organisers

Meinolf Josef Geck University of Aberdeen
Alexander Kleshchev University of Oregon
Gerhard Röhrle Ruhr-Universität Bochum

Speakers

Henning Haahr Andersen Aarhus Universitet
Tomoyuki Arakawa Kyoto University
Michael Bate University of York
Alexander Braverman Brown University
Ken Brown University of Glasgow
Olivier Brunat Ruhr-Universität Bochum
Tim Burness University of Southampton
Anton Gawain Cox City University, London
Charlie Curtis University of Oregon
Corrado De Concini Università degli Studi di Roma La Sapienza
Stephen Donkin University of York
J Matthew Douglass University of North Texas
Michel Duflo Université Paris 7 - Denis-Diderot
Rolf Farnsteiner Bielefeld University
Peter Fiebig Friedrich-Alexander-Universität Erlangen-Nürnberg
Simon Goodwin University of Birmingham
Jeremie Guilhot University of Sydney
Anthony Henderson University of Sydney
David Hernandez CNRS - Ecole Normale Superieure Paris
Gerhard Richard Hiss RWTH Aachen University
Lacrimioara Iancu University of Aberdeen
Nicolas Jacon Université de Franche-Comté
Anthony Joseph University of California, Irvine and Weizmann Institute of Science
Daniel Juteau CNRS - Université de Caen Basse-Normandie
Joel Kamnitzer University of Toronto
Friedrich Knop Friedrich-Alexander-Universität Erlangen-Nürnberg
Laurent Lafforgue IHES
Thomas Lam Harvard University
Emmanuel Letellier CNRS - Université de Caen Basse-Normandie
Paul Levy
Gunter Malle Technische Universität Kaiserslautern
Stuart Martin University of Cambridge
Andrew Mathas University of Sydney
Jean Michel Université Paris 7 - Denis-Diderot
Alexander Ivanovich Molev University of Sydney
Markus Perling Ruhr-Universität Bochum
Goetz Pfeiffer National University of Ireland, Maynooth
Claudio Procesi Università degli Studi di Roma La Sapienza
Claus Michael Ringel Universität Bielefeld
Steen Ryom-Hansen Universidad de Talca
Gary Seitz University of Oregon
Eric Sommers University of Massachusetts
Catharina Stroppel Rheinische Friedrich-Wilhelms-Universität Bonn
Marie-France Vigneras Université Paris 7 - Denis-Diderot
Geordie Williamson University of Oxford
Andrei Zelevinsky Northeastern University

Show All

Programme theme

Preprints

Closed orbits and uniform $\it S$-instability in invariant theory

Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras

On 1-dimensional representations of finite $\it W$-algebras associated to simple Lie algebras of exceptional type

Highest weight categories arising from Khovanov's diagram algebra II: Koszulity

Highest weight categories arising from Khovanov's diagram algebra III: Category $\mathcal O$

Highest weight categories arising from Khovanov's diagram algebra IV: The general linear supergroup

Workshops

Instructional workshop

Algebraic Lie structures with origins in physics

Categorification and geometrisation from representation theory

Spitalfields day: automorphic forms and the Langlands programme

Group theory, geometry and representation theory: Abel Prize 2008

Representation theory and Lie theory

Perspectives in algebraic Lie theory

Seminars

Organisers

Speakers

Supported By

Algebraic Lie theory

Programme theme

Preprints

Closed orbits and uniform $\it S$-instability in invariant theory

Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras

On 1-dimensional representations of finite $\it W$-algebras associated to simple Lie algebras of exceptional type

Highest weight categories arising from Khovanov's diagram algebra II: Koszulity

Highest weight categories arising from Khovanov's diagram algebra III: Category $\mathcal O$

Highest weight categories arising from Khovanov's diagram algebra IV: The general linear supergroup

Workshops

Instructional workshop

Algebraic Lie structures with origins in physics

Categorification and geometrisation from representation theory

Spitalfields day: automorphic forms and the Langlands programme

Group theory, geometry and representation theory: Abel Prize 2008

Representation theory and Lie theory

Perspectives in algebraic Lie theory

Seminars

Organisers

Speakers

Supported By

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