Most of week 3 is dedicated to discussions and collaborations. Below is the schedule for the talks and the reception.
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Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| 10:00-11:00 |
Setia
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Gonin
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Zenkevich
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| 18:00 - |
Reception |
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Titles and Abstracts:
Divya Setia:
Filtration of Tensor Product of Local Weyl Modules for Type A
Let $g$ be a finite-dimensional simple Lie algebra over the complex
field $\mathbb{C}$ and $g[t]$ be the Lie algebra of polynomial mappings
from $\mathbb{C}$ to $g$, which is its associated current Lie algebra.
The notion of Weyl modules for affine Kac-Moody Lie algebras was introduced by
V. Chari and A. Pressley. We study the structure of the finite-dimensional representations
of the current Lie algebra of type $A_n$, $sl_{n+1}[t]$, which are obtained by taking tensor products of two local Weyl modules whose highest weights are multiples of the first and $n$th
fundamental weights. In this talk, we shall determine the graded character of these
tensor product modules in terms of the graded character of local Weyl modules and
prove that these modules admit a filtration whose successive quotients are
fusion products of Demazure modules.
Roman Gonin:
Representations and constructions for toroidal gl_1
I will talk about my projects on toroidal gl_1. The algebra appears in different ways: in the context of Nakajima quiver varieties, deformed W-algebras, Cherednik DAHA, etc. I will first review the necessary background and then present my projects related to this algebra. One of them is on the twisted Fock module, its semi-infinite construction via DAHA, and connection to stable envelope bases. Another project focuses on an exceptionally small representation of this algebra, known as the deformed minimal models, and on the description of their annihilating ideals.
Yegor Zenkevich:
Spiralling R-matrices affine qq-characters and elliptic integrable systems
Using the explicit form of the R-matrices of the quantum toroidal algebra of type gl(1) between a vector and a Fock type representation, I prove two results:
1) Noncommutative Jacobi identity for qq-characters of affine type. This identity relates an infinite product of vertex operators to an infinite sum of qq-characters.
2) Spectral self-duality and mirror symmetry of Noumi-Shiraishi wavefunctions which are conjectured to be eigenfunctions of the nonstationary version of the elliptic Ruijsenaars quantum integrable system.
