Student Representation Theory Seminar is a learning seminar for graduate students in representation theory and related fields.
| Title | Speaker | Date |
|---|---|---|
Generalizations of Chevalley restriction theoremGiven a reductive group G, the classical Chevalley restriction isomorphism allows us to compute G-invariant polynomials on the Lie algebra g in terms of the Weyl group invariant polynomials on the Cartan subalgebra. I will recall this theorem and state its generalizations in several directions. Specifically, I hope to talk about a version of the Chevalley restriction theorem for commuting schemes and a version for symmetric pairs (and if time permits, a version for commuting schemes of symmetric pairs.) |
Pallav Goyal | 22/4/15 |
Gelfand-Tsetlin basesFor certain families of groups, their representations carry a canonical basis (up to scaling) known as the Gelfand-Tsetlin basis. We will expose this theory for the symmetric group, following the paper of Okounkov and Vershik. |
Joshua Mundinger | 22/4/22 |
The Schmid-Vilonen conjecture for irreducible Verma modulesAccording to Harish-Chandra, the problem of deciding whether a representation is unitary or not is very hard. Schmid and Vilonen came up with a conjecture that doesn't solve this problem, but puts it in a "functorial framework". In this talk, I'll explain how to prove the conjecture in the case of irreducible Verma modules. The key will be the usage of a set of coordinates in the flag variety that were introduced by Lu and are motivated by the Poisson structure on the flag variety. |
Anthony Santiago Chaves Aguilar | 22/4/29 |
A Concrete Examination of \(Bun_{\mathbb P^1} GL_2\)In this talk, we will try to give a sense of the “look and feel” of the moduli stack of principal \(G\) bundles; in particular, the case of global curve \(\mathbb P^1\), and structure group \(GL_2\). We will also examine some related stacks, \(Bun_B\) (for a Borel \(B\) in \(GL_2\)) and \(Bun_T\) (for \(T\) a maximal torus in \(GL_2\)), along with the natural maps from \(Bun_B\) to \(Bun_T\) and from \(Bun_B\) to \(Bun_G\). If time permits, we will attempt to give a sense of how these can be used to “geometrize” the classical theory of Eisenstein Series. |
Aaron Slipper | 22/5/6 |
A linear algebraic reconstruction of semisimple Lie algebras from their root systemsI'll give what seems to be a new construction of semisimple Lie algebras from their root data. I'll try to fill in some motivation behind the construction as well as how this naturally arose from the study of companion matrix constructions for the group \(G_2\). If time allows, I may briefly mention some further directions, including a construction of a canonical section of the Chevalley map \(\mathfrak g /G \to \mathfrak g//G\) and a new construction of the Harish-Chandra isomorphism. |
Thomas Hameister | 22/5/13 |
Non-linear Fourier transform and central sheavesThe non-linear Fourier transform is one of the key ingredients in Braverman-Kazhdan’s proposal of proving the standard properties of automorphic L-functions. We will talk about this functor in the setting of D-modules and explain why some desired properties of this functor follow from the study of central sheaves. |
Xinchun Ma | 22/5/20 |
A Compactification of a configuration space for curvesWe will construct, with many pictures, a resolution of the diagonal of the $n$-fold cartesian product of the curve using a sequence of blowups. Then we compute the cohomology of the strata. These constructions serve as a key step in Beilinson and Ginzburg's work on realizing the local structure of $Bun_G$. |
Nikolay Grantcharov | 22/5/27 |