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BIMSA Integrable Systems Seminar
An odd two-dimensional and a three-dimensional realization of Schur functions
An odd two-dimensional and a three-dimensional realization of Schur functions
演讲者
Kohei Motegi
时间
2024年11月19日 16:00 至 17:00
地点
A6-101
线上
Zoom 873 9209 0711
(BIMSA)
摘要
We present unconventional constructions of Schur/Grothendieck polynomials from the viewpoint of quantum integrability.
First, we present a construction of Schur/Grassmannian Grothendieck polynomials using a degeneration of higher rank rational/quantum R-matrices, which is different from the Bethe vector or Fomin-Kirillov type constructions.
Second, using the q=0 version of the three-dimensional $R$-matrix satisfying the tetrahedron equation introduced by
Bazhanov-Sergeev and further studied by Kuniba-Maruyama-Okado, we show that a class of three-dimensional partition functions
can be expressed as Schur polynomials. Keys of our derivation in both constructions are the multiple commutation relations between quantum algebras.
Partly based on joint work with Shinsuke Iwao and Ryo Ohkawa.
First, we present a construction of Schur/Grassmannian Grothendieck polynomials using a degeneration of higher rank rational/quantum R-matrices, which is different from the Bethe vector or Fomin-Kirillov type constructions.
Second, using the q=0 version of the three-dimensional $R$-matrix satisfying the tetrahedron equation introduced by
Bazhanov-Sergeev and further studied by Kuniba-Maruyama-Okado, we show that a class of three-dimensional partition functions
can be expressed as Schur polynomials. Keys of our derivation in both constructions are the multiple commutation relations between quantum algebras.
Partly based on joint work with Shinsuke Iwao and Ryo Ohkawa.