## Infinite Analysis Seminar Tokyo

Seminar information archive ～04/01｜Next seminar｜Future seminars 04/02～

Date, time & place | Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
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### 2018/10/04

16:00-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Integrable quad equations derived from the quantum Yang-Baxter

equation. (ENGLISH)

**Andrew Kels**(Graduate School of Arts and Sciences, University of Tokyo)Integrable quad equations derived from the quantum Yang-Baxter

equation. (ENGLISH)

[ Abstract ]

I will give an overview of an explicit correspondence that exists between

two different types of integrable equations; 1) the quantum Yang-Baxter

equation in its star-triangle relation (STR) form, and 2) the classical

3D-consistent quad equations in the Adler-Bobenko-Suris (ABS)

classification. The fundamental aspect of this correspondence is that the

equation of the critical point of a STR is equivalent to an ABS quad

equation. The STR's considered here are in fact equivalent to

hypergeometric integral transformation formulas. For example, a STR for

$H1_{(\varepsilon=0)}$ corresponds to the Euler Beta function, a STR for

$Q1_{(\delta=0)}$ corresponds to the $n=1$ Selberg integral, and STR's for

$H2_{\varepsilon=0,1}$, $H1_{(\varepsilon=1)}$, correspond to different

hypergeometric integral formulas of Barnes. I will discuss some of these

examples and some directions for future research.

I will give an overview of an explicit correspondence that exists between

two different types of integrable equations; 1) the quantum Yang-Baxter

equation in its star-triangle relation (STR) form, and 2) the classical

3D-consistent quad equations in the Adler-Bobenko-Suris (ABS)

classification. The fundamental aspect of this correspondence is that the

equation of the critical point of a STR is equivalent to an ABS quad

equation. The STR's considered here are in fact equivalent to

hypergeometric integral transformation formulas. For example, a STR for

$H1_{(\varepsilon=0)}$ corresponds to the Euler Beta function, a STR for

$Q1_{(\delta=0)}$ corresponds to the $n=1$ Selberg integral, and STR's for

$H2_{\varepsilon=0,1}$, $H1_{(\varepsilon=1)}$, correspond to different

hypergeometric integral formulas of Barnes. I will discuss some of these

examples and some directions for future research.