## Infinite Analysis Seminar Tokyo

Date, time & place Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.)

### 2015/01/15

15:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Shunsuke Tsuchioka (Graduate School of Mathematical Sciences, the University of Tokyo) 15:00-16:30
On Gram matrices of the Shapovalov form of a basic representation of a
quantum affine group (ENGLISH)
[ Abstract ]
We consider Gram matrices of the Shapovalov form of a basic
representation
of a quantum affine group. We present a conjecture predicting the
invariant
factors of these matrices and proving that it gives the correct
invariants
when one specializes or localizes the ring $\mathbb{Z}[v,v^{-1}]$ in
certain ways.
This generalizes Evseev's theorem which settled affirmatively
the K\"{u}lshammer-Olsson-Robinson conjecture that predicts
the generalized Cartan invariants of the symmetric groups.
This is a joint work with Anton Evseev.
Alexander Tsymbaliuk (SCGP (Simons Center for Geometry and Physics)) 17:00-18:30
Continuous and Infinitesimal Hecke algebras (ENGLISH)
[ Abstract ]
In the late 80's V. Drinfeld introduced the notion of the
degenerate affine Hecke algebras. The particular class of those, called
symplectic reflection algebras, has been rediscovered 15 years later by
[Etingof and Ginzburg]. The theory of those algebras (which include also
the rational Cherednik algebras) has attracted a lot of attention in the
last 15 years.
In this talk we will discuss their continuous and infinitesimal versions,
introduced by [Etingof, Gan, and Ginzburg]. Our key result relates those
classical algebras to the simplest 1-block finite W-algebras.