# Representation Theory Seminar

### Info

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.

### Talks

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.
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.

Books:

### Archive

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