## Infinite Analysis Seminar Tokyo

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

### 2010/09/12

10:30-17:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Hideaki Morita (Muroran Institute of Technology) 10:30-11:30
A factorization formula for Macdonald polynomials at roots of unity (JAPANESE)
[ Abstract ]
We consider a combinatorial property of Macdonald polynomials at roots
of unity.
If we made some plethystic substitution to the variables,
Macdonald polynomials are subjected to a certain decomposition rule
when a parameter is specialized at roots of unity.
We review the result and give an outline of the proof.
This talk is based on a joint work with F. Descouens.
Junichi Shiraishi (Tokyo Univ.) 13:00-14:00
W algebras and symmetric polynomials (JAPANESE)
[ Abstract ]
It is well known that we have the factorization property of the Macdonald polynomials under the principal specialization $x=(1,t,t^2,t^3,¥cdots)$. We try to better understand this situation in terms of the Ding-Iohara algebra or the deformend $W$-algebra. Some conjectures are presented in the case of $N$-fold tensor representation of the Fock modules.
Koji Hasegawa (Tohoku Univ.) 14:30-15:30
Quantizing the difference Painlev¥'e VI equation (JAPANESE)
[ Abstract ]
I will review two constructions for quantum (=non-commutative) version of
q-difference Painleve VI equation.
Yasuhide Numata (Graduate School of Information Science and Technology, Tokyo Univ.) 16:00-17:00
On a bijective proof of a factorization formula for Macdonald
polynomials at roots of unity (JAPANESE)
[ Abstract ]
The subject of this talk is a factorization formula for the special
values of modied Macdonald polynomials at roots of unity.
We give a combinatorial proof of the formula, via a result by
Haglund--Haiman--Leohr, for some special classes of partitions,
including two column partitions.
(This talk is based on a joint work with F. Descouens and H. Morita.)