Infinite Analysis Seminar Tokyo

Seminar information archive ~02/27Next seminarFuture seminars 02/28~

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

2013/05/11

10:30-12:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Anatol Kirillov (RIMS Kyoto Univ.)
Saga of Dunkl elements (ENGLISH)
[ Abstract ]
The Dunkl operators has been introduced by C. Dunkl in the middle of
80's of the last century as a powerful mean in the study of orthogonal
polynomials related with finite Coxeter groups. Later it was discovered
a deep connection of the the Dunkl operators with the theory of
Integrable systems and Invariant Theory.
In my talk I introduce and study a certain class of nonhomogeneous
quadratic algebras together with the distinguish set of mutually
commuting elements inside of each, the so-called universal Dunkl elements.
The main problem I would like to discuss is : What is the algebra
generated by universal Dunkl elements in a different representations of
the quadratic algebra introduced ?
I'm planning to present partial answers on that problem related with
classical and quantum Schubert and Grothendieck Calculi as well as the
theory of elliptic series.
Also some interesting algebraic properties of the quadratic algebra(s)
in question will be described.