## 東京無限可積分系セミナー

開催情報 土曜日　13:30～16:00　数理科学研究科棟(駒場) 117号室 神保道夫、国場敦夫、山田裕二、武部尚志、高木太一郎、白石潤一 https://www.ms.u-tokyo.ac.jp/~takebe/iat/index-j.html

### 2013年02月16日(土)

13:30-15:00   数理科学研究科棟(駒場) 117号室
Alexey Silantyev 氏 (Tokyo. Univ.)
Generalized Calogero-Moser type systems and Cherednik Algebras (ENGLISH)
[ 講演概要 ]
Calogero-Moser systems can be obtained using Dunkl operators, which
define the polynomial representation of the corresponding rational
Cherednik algebra. Parabolic ideals invariant under the action of the
Dunkl operators give submodules of Cherednik algebra. Considering the
corresponding quotient-modules one yields the generalized (or deformed)
Calogero-Moser systems. In the same way we construct the generalized
elliptic Calogero-Moser systems using the elliptic Dunkl operators
obtained by Buchstaber, Felder and Veselov. The Macdonald-Ruijsenaars
systems (difference (relativistic) Calogero-Moser type systems) can be
considered in terms of Double Affine Hecke Algebra (DAHA). We construct
appropriate submodules in the polynomial representation of DAHA, which
were obtained by Kasatani for some affine root systems. Considering the
corresponding quotient representation we derive the generalized
(deformed) Macdonald-Ruijsenaars systems for any affine root system,
which where obtained by Sergeev and Veselov for the A series. This is
joint work with Misha Feigin.