The seminar runs on Thursdays at 3:10pm–4:00pm in Carver Hall 401 at Iowa State University. Talks range from expository given by local speakers, to invited research talks. Themes include

- finite- and infinite-dimensional associative algebras and their modules,
- (quantized) enveloping algebras, Yangians, finite W-algebras, affine Hecke algebras,
- connections to geometry, combinatorics, physics and other fields.

For more information, please contact Jonas Hartwig.

October 26, 2017

TBD

John Dusel (Mount St. Mary's University)

October 19, 2017

TBD, Part 2

Tathagata Basak (ISU)

October 12, 2017

TBD, Part 1

Tathagata Basak (ISU)

October 5, 2017

TBD

Alexander Sistko (University of Iowa)

September 28, 2017

TBD

Richard Kramer (ISU)

TBD

September 21, 2017

Irreducible components of exotic Springer fibers

Daniele Rosso (Indiana University Northwest)

The Springer resolution is a resolution of singularities of the variety of nilpotent elements in a reductive Lie algebra. It is an important geometric construction in representation theory, but some of its features are not as nice if we are working in Type \(C\) (Symplectic group). To make the symplectic case look more like the Type \(A\) case, Kato introduced the exotic nilpotent cone and its resolution, whose fibers are called the exotic Springer fibers. We give a combinatorial description of the irreducible components of these fibers in terms of standard Young bitableaux and obtain an exotic Robinson-Schensted correspondence. This is joint work with Vinoth Nandakumar and Neil Saunders.

Links:
NRS16

September 14, 2017

Canonical Galois orders and maximal commutativity

Jonas Hartwig (ISU)

Galois rings and orders, defined by Futorny and Ovsienko in 2010, form a class of algebras which include many important algebras in representation theory, such as the (quantized) enveloping algebra of \(\mathfrak{gl}_n\), type \(A\) restricted Yangians and finite W-algebras. I will present a new criterion for determining when a Galois ring is a Galois order. This can be applied in particular to \(U_q(\mathfrak{gl}_n)\) which also proves the quantum Gelfand-Zeitlin subalgebra is maximal commutative. This establishes several conjectures including bounds on fibers of irreducible Gelfand-Zeitlin characters. The method in fact applies to all of the mentioned examples and give unified new proofs.

September 7, 2017

Global Weyl modules for non-standard maximal parabolic subalgebras

Matthew Lee (UC Riverside)

In this talk we will discuss the structure of non standard maximal parabolics of twisted affine Lie algebras, global Weyl modules and the associated commutative associative algebras. Since the global Weyl modules associated with the standard maximal parabolics have found many applications the hope is that these non-standard maximal parabolics will lead to different, but equally interesting applications.

August 31, 2017

The current algebra of \(\mathfrak{sl}_2\) and its representations

Jonas Hartwig (ISU)

An introduction to the current algebra of \(\mathfrak{sl}_2\) will be given. This Lie algebra is infinite-dimensional and has non-semisimple finite-dimensional modules (i.e. Weyl's theorem fails). Some classes of modules will be discussed, and open problems in the area stated.

Light reading:

- Applications of Lie theory?
- TWF Week 5 by John Baez. A brief but very enjoyable basic introduction to Lie algebras, representations, quantum groups.
- Basic concepts of Lie algebras by Maths14
- Lie algebra on Wikipedia
- Notes on the classification of complex Lie algebras by Terry Tao

Books:

- Introduction to Lie Groups and Lie Algebras by Alexander Kirillov, Jr.
- Lie Algebras, Algebraic Groups, and Lie Groups by J.S. Milne
- Introduction to Lie algebras and their Representation Theory by Humphreys
- Introduction to Lie algebras by Nicolas Perrin

Date | Speaker | Title | Links |
---|---|---|---|

04/28/17 | Adnan Abdulwahid (ISU) | Nakayama Functor and Quiver Representations | Abstract |

04/07/17 | Miodrag Iovanov (UI) | On Incidence Algebras and their Representations | Abstract |

03/24/17 | JH | Tensor products of representations | |

03/10/17 | JH | Weight modules over noncommutative Kleinian fiber products | Notes Paper1 Paper2 |

03/03/17 | JH | Unitarizable representations | Notes |

02/24/17 | Ben Sheller (ISU) | Lie group actions and stratified spaces | Notes |

02/10/17 | JH | Gelfand-Tsetlin Bases | Notes |

02/03/17 | JH | Parabolic induction | Fernando |

01/27/17 | JH | Simple weight modules over Lie algebras | Mathieu |

01/20/17 | Mark Hunacek (ISU) | Modular Lie algebras | Benkart Rumynin |

12/02/16 | Animesh Biswas (ISU) | The Heisenberg group and its representations | |

11/18/16 | Tathagata Basak (ISU) | Reflection groups II | |

11/11/16 | Tathagata Basak (ISU) | Reflection groups I | Notes |

11/04/16 | JH | What about \(E_9\)? Kac-Moody algebras. | Notes |

10/31/16 | JH | [Comb/Alg Sem] Lie superalgebras and super-differential operators II | |

10/24/16 | JH | [Comb/Alg Sem] Lie superalgebras and super-differential operators I | Notes Kac Serganova |

10/21/16 | JH | Classification of simple Lie algebras | Notes |

10/14/16 | JH | Root space decomposition for \(\mathfrak{sl}(3)\) | |

09/30/16 | JH | Lie algebras and homomorphisms; Examples; Classification problem |
Notes |

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