## Infinite Analysis Seminar Tokyo

Seminar information archive ～04/15｜Next seminar｜Future seminars 04/16～

Date, time & place | Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
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### 2010/09/12

10:30-17:00 Room #117 (Graduate School of Math. Sci. Bldg.)

A factorization formula for Macdonald polynomials at roots of unity (JAPANESE)

W algebras and symmetric polynomials (JAPANESE)

Quantizing the difference Painlev¥'e VI equation (JAPANESE)

On a bijective proof of a factorization formula for Macdonald

polynomials at roots of unity (JAPANESE)

**Hideaki Morita**(Muroran Institute of Technology) 10:30-11:30A 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.

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.) 13:00-14:00W 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.

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.) 14:30-15:30Quantizing the difference Painlev¥'e VI equation (JAPANESE)

[ Abstract ]

I will review two constructions for quantum (=non-commutative) version of

q-difference Painleve VI equation.

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.) 16:00-17:00On 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.)

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.)