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Infinite Analysis Seminar Tokyo
Seminar information archive ～05/22｜Next seminar｜Future seminars 05/23～
| Date, time & place | Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|
2025/04/25
17:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Naoto Okubo (Aoyama Gakuin University, College of Science and Engineering) 17:00-18:00
Cluster algebra and birational representations of affine Weyl groups (JAPANESE)
A generalization of the q-Garnier system with the aid of a birational representation of an affine Weyl group (JAPANESE)
Naoto Okubo (Aoyama Gakuin University, College of Science and Engineering) 17:00-18:00
Cluster algebra and birational representations of affine Weyl groups (JAPANESE)
[ Abstract ]
The cluster algebra (with the coefficients) was introduced by Fomin and Zelevinsky. It is a variety of commutative ring generated by the cluster variables. A set of all cluster variables is given by an operation called the mutation which acts on a triple of the quiver, the cluster variables and the coefficients. Then new cluster variables (resp. coefficients) are rational in original cluster variables and coefficients (resp. coefficients). In this talk, we discuss a systematic formulation of birational representations of affine Weyl groups with the aid of the mutation. These birational representations become sources of the q-Painleve equations as will be seen in the next talk. This talk is based on a collaboration with T. Suzuki (Kindai Univ.) and that with T. Masuda (Aoyama Gakuin Univ.) and T. Tsuda (Aoyama Gakuin Univ).
Takao Suzuki (Kindai University, Faculty of Science and Engineering) 18:00-19:00The cluster algebra (with the coefficients) was introduced by Fomin and Zelevinsky. It is a variety of commutative ring generated by the cluster variables. A set of all cluster variables is given by an operation called the mutation which acts on a triple of the quiver, the cluster variables and the coefficients. Then new cluster variables (resp. coefficients) are rational in original cluster variables and coefficients (resp. coefficients). In this talk, we discuss a systematic formulation of birational representations of affine Weyl groups with the aid of the mutation. These birational representations become sources of the q-Painleve equations as will be seen in the next talk. This talk is based on a collaboration with T. Suzuki (Kindai Univ.) and that with T. Masuda (Aoyama Gakuin Univ.) and T. Tsuda (Aoyama Gakuin Univ).
A generalization of the q-Garnier system with the aid of a birational representation of an affine Weyl group (JAPANESE)
[ Abstract ]
The q-Garnier system was introduced by Sakai as the connection preserving deformation of a linear q-difference equation. Afterward, Nagao and Yamada investigated the q-Garnier system by using the Pade method in detail and gave its variations (regarded as q-analogues of the Schlesinger transformations). In this talk, we formulate the q-Garnier system and its variations systematically by using the birational representation given in the previous talk. If time permits, we discuss a Lax form and a particular solution in terms of the basic hypergeometric series. This talk is based on a collaboration with N. Okubo (Aoyama Gakuin Univ).
The q-Garnier system was introduced by Sakai as the connection preserving deformation of a linear q-difference equation. Afterward, Nagao and Yamada investigated the q-Garnier system by using the Pade method in detail and gave its variations (regarded as q-analogues of the Schlesinger transformations). In this talk, we formulate the q-Garnier system and its variations systematically by using the birational representation given in the previous talk. If time permits, we discuss a Lax form and a particular solution in terms of the basic hypergeometric series. This talk is based on a collaboration with N. Okubo (Aoyama Gakuin Univ).
